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II. Absolute Measurements of a Resistance by a Method based on thato/Lonimz.

By F. E. Smith, A.RC.Sc.

(From the National Physical Laboratory.)

Communicated by R. T. Glazebrook, M.A. y F.R.S.

Eeceived October 27, — Read December 11, 1913,

Principal Contents.

rage

Historical note on the absolute measurement of resistance . 28

Introductory 33

Method of Lorenz . . 35

General description of instrument 38

Motor and fly-wheel 40

Rotating discs and their supports 40

Rotating conducting wires .41

Contact brushes and their lubrication 42

Coil supports 46

Lubrication of bearings . 46

Regulation of speed , . 47

Recording the speed 47

Magnetic tests 49

Construction and measurement of coils 51

Diameters of coils 53

Axial lengths and pitch 61

Erecting and adjusting the instrument 64

Insulation tests 65

Effective diametral distance of segments 66

Measurement of distance between the coils . 68

Calculation of mutual inductance * 70

Correction for conicality . . . . , 76

Correction for variation in pitch 79

Effect of iron of motor . . 81

Arrangement of circuits . 83

Standard resistances used 86

Setting of coils to be co-axial 87

Determination of resistance in absolute measure 93

Probable errors 99

Conclusions. 107

VOL. OOXIY. A 510. E 2 Published separately, March 19, 1914.

28 MR. F. E. SMITH ON THE ABSOLUTE MEASUREMENTS OF A

Historical Introduction,

There are many methods by which a resistance can be measured absolutely in the
electromagnetic system of units, and all of these necessarily involve absolute measure-
ments of a length and of a time. The length may be the axial length or radius of a
coil, or the radius of a disc, or it may involve all of these, and the time may be the
time of vibration of a magnet, or of a rotation of a coil, or of the period of an
alternating current. In any case, the precision secured in the measurement of a
resistance depends primarily on the accuracy obtained in these measurements of
length and of time.

The first absolute measurements # of a resistance were made by KiRCHHOFFf in
1849, but it is to W. Weber J that we owe the first distinct proposal (in 1851) of a
definite system of electrical measurements according to which resistance can be
measured in terms of an absolute velocity.

Weber devised three methods by which the resistance of a wire can be determined
absolutely, and he published the results of experiments by two of these. The first
was by means of an earth inductor, and the second by observing the damping of a
swinging magnet, the results obtained differing among themselves by 5 parts in 1900.
In 1853§ he made a determination of the specific resistance of copper, but the experi-
ments were made more to develop the methods than for exact measurements.

In 1862 Weber 1 1 made a more exact determination of resistance using a method
compounded of his first two methods and eliminating the constant of the galvano-
meter. The results of these experiments were embodied in a determination of the
value of the Siemens unit and of a standard coil sent to him by Sir William
Thomson, but the unit obtained was about 8 per cent, less than the 1863 unit of the
British Association Committee on Electrical Standards. 1T

The measurements made by Maxwell, Fleeminc Jenkin, and Balfour Stewart
for the British Association Committee, although subsequently found to be incorrect
by nearly 1*5 per cent., are the first with any claim to precision. The method
adopted by these experimenters is that of the rotating coil and was devised by
Prof. Thomson (later Lord Kelvin) independently, we believe, of a prior suggestion
by W. Weber. The apparatus consists of a short-circuited coil rotating about a

*

* Admirable summaries and criticisms of various methods will be found in Wiedemann's ' Electricitat/
vol. IV., p. 910; Mascart and Joubert's * Lemons sur PElectrieite/ II., p. 581; Lord Rayleigh, 'Phil.
Mag./ 1882; Wiedemann, 'Phil. Mag./ 1882; Glazebrook, 'Electrician/ 1890; Dorn, ' Wissenschaft-
liche Abhand. der Phys. Techn. Reichsanstalt/ vol. II., p. 357, 1895.

t "Bestimmung der Constanten von welcher die Intensitat inducirter elektrischer Strome abhangt,"
<Pogg. Ann./ Bd. 76, S. 412.

J ' Elektrodynamisehe Maassbestimmungen/ or ' Pogg. Ann./ Bd. 82, S. 337.

§ ' Abh. d. Kon. Ges. d. Wissenschaften zu Gottingen/ Bd. 5.

|] 'Zur Gal vanometrie/ Gottingen, 1862.

51 'Eeports of B.A. Electrical Standards Committee/ 1863.

RESISTANCE BY A METHOD BASED ON THAT OF LOEENZ. 29

vertical axis in the earth's magnetic field. Currents are induced in the coil and these
produce a deflection of a small magnet suspended at the centre. The dimensions of
the coil and the time of its rotation being known, the resistance of the wire of
the coil can be calculated. This method was also used by Lord Rayleigh and
Prof. Schuster* in 1881, by Lord Rayleigh t in 1882, and by W. WeberJ also in
1882. The results are given in Table I.

In the method of the earth inductor due to W. Weber a coil is mounted on a
vertical axis with the mean diametral plane in the magnetic meridian. In circuit
with the coil is a ballistic galvanometer through which a quantity of electricity flows
when the coil is quickly turned through half a revolution. The resistance of the
whole circuit can be calculated from the dimensions of the coils, the constants of the
galvanometer, and the deflection produced by the half rotation of the coil. Methods
based on this inductor principle have been used by F. Kohlratjsch and G. Wiede-
mann. §

In a third method used by Kirchhoff, two coils, between which, there is a mutual
inductance, are joined up in series with a battery and galvanometer, and a resistance,
R, joins the junction of the two coils to a point on the circuit between the galvano-
meter and battery. The steady current deflection of the galvanometer is first
observed and then the throw due to one of the coils being removed to a position in
which the mutual inductance is zero. The dimensions of the coils and the constants
of the galvanometer enable the resistance R to be calculated. Methods based on this
inductive principle have been used by Rowland, || Glazebrook,1T and Mascart,
de Nerville, and Benoit. ## Many of the developments of the method are of
extreme importance, and, except for the essential principle being the same, there is
little in common. Similar remarks apply also to the developments of other methods.

The method adopted by RoiTift and HimstedtJJ is somewhat similar to that of
Kirchhoff, but, instead of having to observe the deflection due to a single impulse, a
constant deflection due to a series of impulses is obtained. The current through one
of the fixed coils is made and broken n times per second, and the galvanometer
circuit is made only on the make or break of the current. The method adopted by
Guillet §§ belongs in part to this class and in part to the method suggested by

LlPPMANN.

* Eayleigh and Schuster, 'Roy. Soc. Proc./ vol. 32, 1881.

t Eayleigh, 'Phil. Trans.,' vol. 173, 1882.

J Weber, ' Der Eotationsindukfcor,' 1882.

§ G. Wiedemann, £ Abh. der BerL Ak.,' 1884.

|| Eowland, 1876, 'Physical Papers,' pp. 145-239; The Johns Hopkins Press, 1902.

H Glazebrook, 'Phil. Trans.,' vol. 174, p. 223, 1883.

** Mascart, de Nerville, and Benoit, 'Ann. de Chemie et de phys.,' VI., p. 1, 1885.
ft Eoiti, 'Nuovo Cimento/ III., 15, 1884.

It Himstedt, 'Berichte der Naturforschenden Ges. zu Freiburg i. B.,' Heft I, 1886.
§ GmLLftr, ' Journ. de Physique,' 8, pp. 471-477, 1899.

30 ME. F. E. SMITH ON THE ABSOLUTE MEASUREMENTS OF A

Another method used by Weber is commonly called the method of damping. A
magnet is suspended within a coil and set in oscillation (a) when the circuit is open,
and (b) when the circuit is closed. The periods and logarithmic decrements are
observed, and from a comparison of the results the resistance of the coil can be
calculated. This method was used by Weber and with important modifications by
Dorn, # WiLD,t and Kohlrausch.J

In the method due to Lorejstz§ a metallic disc is rotated at a constant rate in a
magnetic field produced by a current which circulates through a coil co-axial with
the disc. The disc is touched at its circumference and centre by two wires, and the
difference of potential is balanced against that at the extremities of a resistance, R,
the current through which is the same as that circulating through the coil. When the
mutual inductance of the coil and disc circumference, and the rate of rotation of
the disc are known, the resistance R can be calculated. Methods based on this
principle have been used by Lorenz, || Lord Rayleigh and Mrs. Sidgwick,!
Rowland and Kimball, ## Duncan, Wilkes, and Hutchinson, ft Jones,JJ and
Ayrton and Jones.§§

Foster, 1 1 1| and afterwards Lippmann,!! suggested the use of a rotating coil, but
contact with the extremities of the coil was made only at the moment when the
induced voltage was a maximum. The induced voltage is balanced by that due to an
external current (which may produce the field in. which the coil rotates) through a
known resistance. Observations by a method based on this principle have been
carried out by Lippmann and Wuilleumier. ###

The most recent determination of a resistance in absolute measure is due to
A. Campbell. ttt In Campbell's experiments two very nearly equal alternating
currents in quadrature, taken from a two-phase alternator of sine-wave voltage, are
passed through a resistance R and the primary circuit of a variable mutual
inductance respectively. The ratio of these two currents is measured by passing
them through equal resistances and comparing the deflections on an electrostatic

* Dorn, ' Wied. Ann.,' 17, 1882, and 36, 1889.

f Wild, 'Mem. de l'Ac. des Sc. St. Petersburg,' tome 32, Nro. % 1884.

X Kohlrausch, ' Abh. der bayr. Ak. d. W./ Bd. 16, 1888.

§ Lorenz, 'Pogg. Ann.,' 149, p. 251, 1873.

|| Lorenz, 'Wied. Ann.,' 25, p. 1, 1885.

H Lord Kayleigh and Mrs. Sidgwick, 'Phil. Trans.,' vol. 174, p. 295, 1883.
** Eowland and Kimball, 'La Lumiere Electrique/ vol. 26, pp. 188, 189, 477, 1887.
tt Duncan, Wilkes, and Hutchinson, 'Phil. Mag./ p. 98, 1889.
%X Jones, 'Electrician,' p. 552, 1890. Also 'B.A. Electrical Standards Reports/ 1893, 1894.

§§ Ayrton and Jones, ' B.A. Electrical Standards Reports/ 1897.

Jill G. Carey Foster, 'B.A. Electrical Standards Reports/ 1870.
UH Lippmann, 'Comptes Rendus/ 95, p. 1348, 1882.
*** Wuilleumier, 'Journal de Physique/ 11, 9, p. 220, 1890.
ttt Campbell, 'Roy. Soc. Proc./ 87, 1912.

EESISTANOE BY A METHOD BASED ON THAT OF LORENZ, 31

voltmeter placed across either resistance. The voltage across the resistance R is
balanced (by the help of a tuned vibration galvanometer) against the voltage induced
in the secondary circuit of the mutual inductance. The value of the variable mutual
inductance is found by comparison with a fixed mutual inductance whose value is
calculated from its dimensions, and the resistance R is determined in terms of this
inductance and the frequency of the alternating current.

Table I. gives the principal results, the values given in columns 5, 6, and 7 being
those given by the experimenters. It will be seen that in some cases mercury
standards of resistance were available, and in other cases the results are given in
terms of the British Association unit (B.A. unit) or the Siemens unit. When
mercury standards of resistance were available, the results (previous to 1892) state
the length at 0° 0. of a column of mercury having a uniform cross-section of
1 sq. mm. and a resistance of 1 ohm. The Siemens unit of resistance is the resistance
at 0° C of a column of mercury 100 cm. in length and 1 sq. mm. in cross-section;
results which give the absolute value of the Siemens unit may therefore be reduced
to give the length representing 1 ohm by taking the reciprocal of the absolute value
and multiplying by 100.

In 1892, and again in 1908, the international ohm was defined as the resistance of
a specified column of mercury. In 1892 Dr. von Helmholtz pointed out that a
difficulty arose in determining the cross-section of a column of mercury owing to
there being some doubt as to the correct value for its density. He suggested that
the difficulty should be avoided by stating the mass of a mercury column of a given
length which has a resistance of 1 ohm. This was agreed to and the international
ohm was defined as the resistance at 0° C. of a column of mercury 14*4521 gr. in
mass and having a length of 106*3 cm. The number 14*4521 is the product of 1*063
and 13*5956, the latter number representing at that time the mean of the best
determinations of the density of mercury at 0° C. The cross-section of the specified
column is therefore equal to 1 sq. mm. or nearly so. The ratio of the international
ohm to the Siemens unit may therefore be taken as 1*063.

The B.A, unit is so much referred to in the earlier determinations that it may be
useful to state clearly what is meant by the unit. In 1864 Messrs. Matthiessen and
Hockin constructed a number of coils of various materials to represent at certain
specified temperatures resistances of 10 9 cm./sec. units of resistance as determined by
the 1862-3 British Association Committee on Electrical Standards. The resistances
of these coils did not keep absolutely constant, and in after years the B.A. unit was
taken as the mean of the values of six of these coils at the temperature at which they
were stated by Hockin to be correct. The B.A. unit of one period is not, therefore,
necessarily the same as that of another period. Every precaution was, of course,
taken to ensure constancy, but with wire standards of resistance great difficulty is
experienced. In after years # it proved possible to trace the changes in these coils

* ' B.A. Elec. Stands. Committee Keport/ 1908.

32 MR F. E. SMITH ON THE ABSOLUTE MEASUREMENTS OF A

with what appears to be a fair measure of success, and the corrections due to changes
in the coils can in certain cases be calculated.

It follows, therefore, that if the B.A. unit of any particular period is known in
terms of the resistance of a column of mercury, and if the coils used for the absolute
measurements remained constant in resistance from the time of their measurements
in terms of a mercury column to the time of their absolute measurement, the results
given in Table I. can in all cases be reduced to give the length of the column of
mercury having a resistance of 1 ohm.

But it is very probable that the resistance of many of the coils did not keep
constant, and it is not possible for us to reduce the results except in a few cases.
The instances referred to are the determinations by Lord Rayleigh, by Dr. Glaze-
brook, by Viriamu Jones, and by Ayrton and Jones. In all of these cases
comparisons were made with the B.A. standard coils, and the details of these
comparisons have been preserved and published. In the Report of the B.A. Electrical
Standards Committee for 1908, the changes in resistance of the coils used by Lord
Rayleigh and Dr. Glazebrook have been traced, and a comparison of the mercury
standards of resistance made by Lord Rayleigh, Dr. Glazebrook, and F. E. Smith
is given in Table VIII. of the same report. This comparison, together with the notes
on the standards used, enables us to express Lord Rayleigh's and Dr. Glazebrook's
results in terms of the present mercury standards of the National Physical Laboratory,
This we have done, the results being marked (S), while (A) indicates the results given
by the author.

Referring first to Lord Rayleigh's determination in 1882, we find that
comparisons were made with certain B.A. unit coils and with mercury standards of
resistance. However, the terminals of the latter were not at 0° C. but between 5° C.
and 6° C., and it was shown by Dr. Glazebrook in 1888 that an error of 24 parts
in 100,000 was introduced because of this. If we apply a correction of this
amount, Lord Rayleigh's 1882 value of the ohm in centimetres of mercury becomes
106*24 (1 4-0-00024) = 106*26 5 , and the 1883 value becomes 106'214 (l + 0*00024)
= 106*239. These values are given in Table I. (within 1 part in 10,000) as 106*26
and 106*24.

Dr. Glazebrook's determination of the ohm was made in 1882, and he constructed
mercury standards of resistance in 1888. The principal resistance coil employed in
1882 was a platinum-silver coil known as " flat," and this also was used in 1888. In
the interval it was assumed to have kept constant — there was at that time no certain
evidence to the contrary. A careful survey of the history of the coils, which is
published in the B.A. Beport for 1908, shows, however, that "flat" increased in
resistance in the interval 1882-1888 by 41 parts in 100,000. Dr. Glazebrook^
value for the ohm in centimetres of mercury is 106*29, and this, when corrected for
the change in the resistance coils, becomes 106*29 (1 — 0*00041) = 106*25.

The coils used by Viriamu Jones in 1894 were compared with the B.A. standards

RESISTANCE BY A METHOD BASED ON THAT OF LORENZ. 33

by Dr. Glazebrook. One of these coils was No. 3715, and its value in 1894 was
stated by Dr. Glazebrook to be r00026 ohms (international) at 14°'95 C, the
relation between the B.A. unit and the ohm (international) being taken as
1 ohm = 1*01358 B.A. unit. # From the results obtained at the N.P.L. in 1908 we
conclude that this coil increased in resistance in the interval 1894-1908 by 7 parts in
100,000. Its value in 1908 was measured to be 1*00066 international ohms at
16°'0 C. or 1*00034 international ohms at 14°*95 C When allowance is made for the
rise in resistance of 7 parts in 100,000, it will be seen that the difference from
Dr. Glazebrook's value is 1 part in 100,000. We conclude, therefore, that the value
given by Viriamu Jones in 1894 is not in error because of any uncertainty in the
values of the resistance coils used.

Similarly we have investigated the coils used by Ayrton and Jones in 1897, and
we find the values in Board of Trade ohms agree with the values in international ohms
within 1 or 2 parts in 100,000.. We conclude, therefore, that the length of the column

-I A/? • Q AA

of mercury representing the ohm is (from their experiments) — ; = 106*274 cm.

Unfortunately, we are not sufficiently acquainted with the standards used by other
investigators to reduce their results, and in the last column of the table the results
given, except for the cases already dealt with, are those only in which mercury
standards were available.

Section 1. — Introductory.

The instrument described in this paper is the outcome of a desire expressed by the
late Prof. J. Viriamu Jones at a meeting of the British Association Committee on
Practical Electrical Units and Standards, in 1893. Prof. Jones expressed the hope
that in the near future there might be constructed an apparatus based on the method
used by Lorenz, which would be kept in constant use in a national laboratory
and embody in concrete form a proper ultimate standard of electrical resistance.

In 1900 the Drapers Company of London promised to Prof. Jones the funds for
the construction of such an instrument, and after Prof. Jones's death in 1901 the
Company placed £700 at the disposal of the Executive Committee of the National
Physical Laboratory in order that the instrument might be made.

The apparatus was to be in memory of Prof. Jones, and to be constructed under
the superintendence of the late Prof. Ayrton and of Dr. Glazebrook. Delay in
proceeding with the work arose owing to the construction of the Ayrton-Jones
current balance, and it was not until after completion of the balance in 1907 that a
start was made. Unfortunately, Prof. Ayrton was in very poor health, and
although keenly interested in the work he did not live to take any part in it.

The form of apparatus eventually decided on was considerably larger than
anticipated in 1893. The metal work was much too heavy for machining in the

* ' B.A. Elec. Stands. Committee Reports/ 1892 and 1894.
VOL. COXIV. — A. F

34

ME, F. E. SMITH ON THE ABSOLUTE MEASUREMENTS OF A

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RESISTANCE BY A METHOD BASED ON THAT OP JLOKENZ. 35

Laboratory workshops, and Sir Andrew Noble, F.R.S., was approached with a view
to this part of the instrument being made in the workshops of Sir W. G. Armstrong,
Whitworth & Co. at Elswick. Sir Andrew Noble not only undertook that this
should be done, but took such a keen interest in the work that he generously provided
it at very much less than the cost price.

Lorenz apparatus made for Prof. Callendar by Messrs. Nalder Bros. & Co.
Although we were unable to take much advantage of this opportunity owing to the
big difference in the designs of the two instruments, we desire to express our thanks
to Messrs. Nalder Bros, for their kindness.

The instrument herein described possesses many new features of importance. It is
permanent, but determinations of resistance made from time to time will not assume
constancy of any dimensions ; it is comparatively easy to use, and the results obtained
are believed to be of high precision.

Section 2. — The Method of Lorenz.

In this method, which was first employed by Lorenz^ in 1873, a rotating disc is
placed in a magnetic field produced by a current which circulates through a coil
coaxial with the disc. In the apparatus used by Lorenz wire brushes made contact
with the disc at its circumference and centre, and the circuit was closed by connecting
the brushes, through a galvanometer, with the extremities of a resistance R. The
voltage induced by the uniform rotation of the disc at n revolutions per second is
Mm, where M is the mutual inductance of the coil and a circle coincident with the
edge of the disc, and i is the current through the coil. This induced voltage is
balanced against the difference of potential Bi between the extremities of the
resistance R through which the same current flows as through the coil. When
equality of voltage is indicated by the galvanometer R = nM.. M is calculated from
the dimensions of the coil and disc and thus R is found. The coil used was of a large
number of turns in order to make M as great as possible.

In the 'Philosophical Magazine' for November, 1882, Lord Rayleigh compares
the method of Lorenz with other methods. After stating that he is disposed to
consider Lorenz's method the best, he proceeds to deal with some of the difficulties.
The first of these is the smallness of the resistance R which can be directly measured,
and this led Lord Rayleigh to adopt a system of shunted resistances which, for part
of our work, we also have used. Lord Rayleigh remarks that the influence of
terrestrial magnetism and the thermo-electric effects at the sliding contacts are both
very appreciable and give rise to trouble during the observations, but they can be
eliminated by observing only the effect of reversing the battery current.

The more important portion of Lord Rayleigh's comments deals with the ratio of

* Lorenz, < Pogg. Ann.,' 149, p. 251, 1873.

E 2

36 ME. F. E, SMITH ON THE ABSOLUTE MEASUREMENTS OF A

the dimensions of the coil and disc. The results are given of some calculations of the
mutual inductance M of a coil of radius A and circle of radius a. The rates of
variation of M with change in the diameter of the coil are calculated for various
values of a/A, and it is shown that when a/A increases in value the rate of variation
of M with change in a and also of A increases. Further, it is shown that, by using
two coils separated to a considerable distance, it is possible so to proportion the radii
and the distance apart of the coils that the error of mean radius of the coil does not
affect the result ; the diameter of the disc and the distance apart of the two coils are
then the important quantities. Lord Rayleigh remarks : " It is clear that M
vanishes both when A is very small and when it is very large ; from which it follows
that there must be some value of A for which the effect is a maximum and therefore
independent of small variations of A." The same is, of course, true for the disc ; by
suitably proportioning the dimensions, the error of mean radius of the disc may be
rendered negligibly small. This fact led Mr. A. Oampbell # to design a standard of
mutual inductance in which the radius of the secondary is not required to be known
with great precision ; it also guided us in fixing the dimensions of our coils and discs
so that the diameters of the latter need not be accurately known.

In the first and second series of experiments carried out by Lord Rayleigh the
inductance coils were situated nearly in the plane of the revolving disc as in Lorenz's
original use of the method. In the third series the coils were separated from the
disc to such a distance as to render the accuracy of the results practically independent
of the mean radius of the coils. It is right to say here that in the design of the
apparatus described in this paper we were largely influenced by Lord Rayleigh's
investigations and by Mr. Campbell's work.

Of the experimental difficulties noted by Lord Rayleigh the more important are :
(l) troublesome thermo-electric effects at the sliding contacts notwithstanding that
the edge of the disc was amalgamated with mercury, and (2) effects due to terrestrial
magnetism. As before stated, both of these effects are eliminated by taking a
sufficient number of readings with reversals of the current, but it is evident that good
readings cannot be taken if the magnitude of the effects is subject to sudden
fluctuation.

In 1890 Prof. J. V. Jones t made a number of suggestions towards a determination
of the ohm. He had made a number of experiments in his laboratory at the
University College, Cardiff, and stated that he was of opinion that, if apparatus were
constructed on a large scale and with a certain perfecting of detail, a single set of
observations would give a result accurate within 1 part in 10,000. In the electrical
observations the principal difficulties which he had contended with were: (l) varia-
tions in the thermo-electric effects at the brush contacts, and (2) variations in the
rate of rotation of the disc. A considerable reduction of the first difficulty was

* Campbell, ' Roy. Soc. Proc./ A, vol. 79, p. 428.
t Paper read before the British Association, 1890.

RESISTANCE BY A METHOD BASED ON THAT OF LORENZ. 37

brought about by using a brush consisting of a single wire perforated by a channel
through which a constant flow of mercury was maintained. With regard to the
variation of speed, Prof. Jones was of opinion that " no time or trouble spent in
securing a constant speed will be lost for the purpose in view." It was suggested
that the standard coil should consist of a single layer of wire, as the mutual
inductance of the coils and disc could then be calculated with great accuracy.

The apparatus made by Messrs. Nalder Bros. # for Prof. Callendar, who was then
at the McGill University, Montreal, was, in general arrangement and dimensions,
similar to Prof. Jones's Cardiff apparatus. Contact with the edge of the disc was
made by three small tangential phosphor-bronze tubes lightly pressed on it, at points
separated by angular distances of 120 degrees, and through these tubes mercury
flowed on to the edge of the disc. The employment of three brushes was suggested
by Rowland to eliminate small errors due to imperfect centering of the coil and disc,
and was a distinct improvement. The possible sources of error were considered, and
in a paper by Prof. Ayrton and Prof. Jones # an equation is given showing the rates
of variation of the mutual inductance of the coil and disc with changes (l) in the
radius A of the coil, (2) in the radius a of the disc, and (3) in the axial length 2x of
the helix. The equation given is

^= 1-246 ^+2-346 — -0-0997— .

M A a x

The value of M was 45814*5 cm., of A 267039 cm., and of a 16*5354 cm., from which
it is readily calculated that an error of 0'002 cm. in the measurement of the diameter
of the disc introduced an error of nearly 5 parts in 100,000 in the value of M. An
error in the measurement of the diameter of the coil of 0*002 cm. introduced an error
of 14 parts in 100,000 in the value of M.

It will be seen that the experimental difficulties experienced by observers using the
Lorenz method were mainly due to thermo-electric troubles at the brush contacts,
want of uniformity of speed, and the effect of terrestrial magnetism. There are no
difficulties attendant on the accurate evaluation of the mutual inductance of a coil
and disc if the dimensions are accurately known. If a single layer coil is used, its
dimensions may be determined with great accuracy ; if a coil of many layers is
employed, it appears best to follow Lord Rayleigh's practice and use two coils at a
considerable distance apart in order that errors of measurement of the radius of a coil
may be rendered negligibly small.

The Lorenz apparatus described in this paper was designed in 1908, our object being
to determine a resistance in absolute- measure with a precision within a few parts in
a hundred thousand. The apparatus described eliminates the effect of terrestrial
magnetism and largely reduces thermo-electric troubles at the brush contacts by the
employment of two discs of equal diameters. The coils are of one layer only and

* i

British Association Reports/ 1897.

38

MR. F. E. SMITH ON THE ABSOLUTE MEASUREMENTS OF A

their dimensions, together with those of the discs, may be determined with ease and
with precision ; in addition, any possible error in the measurement of the diameters of
the discs is made negligibly small. Instead of employing one rotating conductor, a
number are used, and the induced voltages may be placed in parallel or in series. The
machine is of the best construction, great attention being paid to lubrication in order
to avoid irregularities in the speed. As already stated, the heavy metal work was
kindly undertaken by Sir W. G. Armstrong, Whitworth & Co,, but the smaller work
such as the chronograph, commutators, brushes, coil fittings, &c, many of which
demanded great skill in their construction, were made by Mr. F. H. Murfitt, who
has charge of the instrument shop of the Laboratory, and whom we also thank for
many suggestions,

Section 3. — General Description.

The instrument consists of two metallic discs which support ten conducting wires
rotating in a magnetic field produced by a current in four coils ; an electric motor is
used as the source of power. Phosphor-bronze wire brushes make contact with
segments made of the same alloy attached to the ends of the rotating wires, and the
difference of potential between the brush contacts at the ends of a single wire, or that
between five wires, is balanced against the difference of potential between two points
on a standard resistance, the current through which is the same as that flowing through
the four coils, A diagrammatic sketch of the arrangement is shown in fig. 1.

Fig. 1.

It will be seen that the current in the coils 1 and 2 is in the opposite direction to
that in the coils 3 and 4. The resulting magnetic fields are opposed in direction, and
the value of the field at points in the neighbourhood of the edge of a disc is zero
or nearly so. A difference of potential is produced between the ends of a rotating
conductor, and its value is dependent on the position only of the ends of the

RESISTANCE BY A METHOD BASED ON THAT OF LORENZ. 39

conductor and not upon its shape, conditionally that the conductor passes through the
coils carrying the current. Thus the difference of potential at the extremities of a
conductor ACDB is not altered if its shape is changed to AEFB. The segments
which form the ends of the conductors are insulated from each other and from the
discs,

The brushes consist of phosphor-bronze wires stretched by two spiral springs, and
resemble violin bows. Each brush makes contact with one or two segments over a
length varying from 5 to 6 cm., and leaves a segment at a tangent thus making the
pressure greatest at the mid-point of contact. Petrol is employed as a lubricant.

There are two principal ways of using the apparatus. In the first the ten brushes
are included in a circuit so as to be in series. When each brush is in contact with a
single segment, the differences of potential due to five rotating conductors are added
together, the remaining five conductors being ineffective. When each brush connects
two neighbouring segments the ten rotating conductors are arranged in five sets of
two in parallel and the total potential difference is the same as before. It is easily
seen that by having a comparatively large arc of contact between each brush and a
segment (or segments) and twice as many segments as brushes, the circuit made
through the brush contacts is never broken.

In the second method, the brushes are divided into two sets of five in parallel and
the total potential difference is the same as that of a single rotating conductor.

All the coils are wound with bare copper wire on hollow marble cylinders having
double-threaded screw grooves cut on the surfaces. The two wires on any one
cylinder form two adjacent helices which may be connected in series or in parallel.
In the general use of the instrument they were connected in series, but they may at
any time be disconnected from each other and an insulation test made between them.
There are eight helices in all and these are connected by means of small concentric
cables to a plug board and commutators which enable the direction of the current in
any coil to be changed at will.

Each of the cylinders is mounted on a strong metal support and its position with
regard to a disc may be altered with ease by screw adjustments. The distance
between the mid-planes of two coils is measured by means of microscopes.

The electric motor used for driving is situated at a considerable distance from any
one of the coils, and its influence on the result was calculated and also experimentally
proved to be negligibly small. A commutator is fixed to the axle of the motor, and
this serves to charge and discharge a condenser placed in one arm of a Wheatstone
bridge. By keeping the bridge permanently balanced, the speed of the Lorenz
apparatus is maintained constant. A directly driven chronograph enables the speed
to be calculated.

The whole instrument is supported on gun-metal rails embedded in a solid block
made with Keene's cement, sand, and ballast. With the exception of the motor, no
magnetic material is used in the construction of the apparatus or supports. The

40

ME. F. E. SMITH ON THE ABSOLUTE MEASUREMENTS OF A

complete apparatus is diagrammatically shown in fig. 2 ; fig. 3 is a photograph of the
instrument taken from the end farther from the motor. The overall length is seven
metres.

ivi w o , o

_J — *| J— — "L

^c:.'.„.„

™.-/

r^fix.

HIK7=

i

c =(-HD==q

V-* h

\^ —.--J LummJ

Fig. 2.
M, motor ; W, fly-wheel ; DD, discs ; CCCC, coils on cylinders.

Section 4. — The Motor, and Fly-wheel.

The electric motor M, fig. 2, is coupled to a shaft supporting a fly-wheel W; the
fly-wheel shaft is in turn coupled to another supporting one of the discs, and the latter
shaft is coupled to a similar one supporting the other disc. The coupling between the
fly-wheel shaft and that supporting one of the discs is an insulating one, washers and
tubes of stabilit being used to secure good insulation.

The electric motor is a shunt- wound one supplied by Messrs Crompton & Co., Ltd.
The machine has four poles and has a commutator of the radial type. The shaft is of
phosphor bronze and the motor is mounted on a base of the same alloy in order to
reduce the quantity of magnetic material to a minimum. The stray field of the
motor in an axial direction is surprisingly small, its intensity at a distance of 400 cm.
amounting to 0*0006 C.G.S. units only. Our original intention was to enclose the
motor in a double shell of soft iron, and the base of such a shell is interposed between
the motor and its support; the results of our observations on the stray field showed
this to be unnecessary and the idea was abandoned. The effect of the motor on the
mutual inductance of the coils and discs is discussed in Section 19.

The fly-wheel is of phosphor bronze. The outer diameter is 50 cm. and the weight
of metal in the rim is about 80 kgr.

Section 5. — The Rotating Discs and Their Supports.

The portion to the right of the instrument (fig. 2) consists of two similar parts, and
only one of these will be described. Fig. 4 shows one of the parts.

The disc D is of rolled phosphor bronze fitted on a shaft S made of an alloy of
copper and aluminium (10 per cent, aluminium and 90 per cent, copper). The
original intention was to have the shaft of phosphor bronze, and two such shafts were
made but were rejected on account of their appreciable magnetic susceptibility.
Phosphor-bronze billets having the requisite magnetic properties could readily be
obtained, but in such cases they failed to give satisfactory results with the mechanical
tests and were therefore unsuited for shafting. The diameter of a disc is about 53 cm.,
and that of the shaft is 5 cm.

F. E. Smith

Phil. Trans., A, vol. 214.

Fig. 3.

Fig. 4.

To face p. 40.

RESISTANCE BY A METHOD BASED ON THAT OF LOEENZ. 41

The shaft runs in bearings made of a special alloy of tin (69 per cent.), zinc (29*6
per cent.), and copper (1*4 per cent.), this being the best non-magnetic alloy we know
of in which a copper aluminium shaft will run without trouble. The pedestals PP and
bed B, supporting the bearings, are of phosphor bronze, except for slabs of stabilit
T, 6 mm. in thickness, which insulate the bearings from the bed. The upper part of
a pedestal is bolted to the lower part by phosphor-bronze bolts L, stabilit washers
W, and stabilit tubes being used to insulate the upper and lower parts. The insulation
resistance between the shaft and the bed has been measured on many occasions, but
has never been less than a thousand megohms. If two metallic discs with uninsulated
rims and conductors are employed, such insulation is essential, but it is not necessary
with insulated conductors and segments such as we have used.

The oil feed (F) and return pipes (R) are of copper and are insulated from the
pedestal by glass and ebonite tubes and oil-resisting rubber washers. Oil throwers
are fitted to the shaft and effectually prevent the oil travelling outwards from the
bearings.

Section 6. — The Rotating Conductors which Pass from the Edge of One

Disc to the Edge of the Other Disc.

We have already briefly described the system of ten conducting wires passing from
disc to disc, and it will be realised that the discs in the present apparatus serve only
to support the radial conductors and are employed for no other purpose. The wires
used consist of No. 26 double silk-covered copper wire, shellacked, and covered with
silk tube.

In order to place the ten wires in position, the shaft was drilled centrally and
parallel to its length from the coupling between the two discs to points within 20 cm.
of the discs, and radial holes were drilled in the shaft in these latter positions. On
the coupling between the discs blocks of ebonite are screwed, and these support
terminals to which the ends of the wires can be attached. Ten wires pass from the
segments attached to the edge of one disc, through a channel milled in the side of the
disc, and again through a brass tube screwed on the shaft, into a radial hole ; after
passing through the central hole drilled in the shaft they emerge at the coupling, and
the free ends of the wires are attached to terminals on the ebonite blocks. Similarly,
ten wires pass from the edge of the other disc to corresponding terminals, and by
making suitable connections between the terminals we obtain a system of ten
conductors which pass between the segments on the two discs. As already explained,
the path of the conductors is unimportant, conditionally that they pass through the
coils.

On the edge of a disc ten segments of stabilit are screwed. Some of these can be
seen in the photograph (fig. 3), and in the sketch (fig. 5) ; a sectional view of a
segment attached to a disc is shown in fig. 5c. On emerging from the channel milled

VOL. CCXIV. — A. G

42

MR. F. E. SMITH ON THE ABSOLUTE MEASUREMENTS OF A

in the disc, the wires pass along a groove G, milled in the stability and are soldered to
ten phosphor-bronze wire segments, of square section, which are screwed to the stabilit
in the manner shown in the illustration. This method was adopted because of the
strain to which the segments are subjected when the machine is running at full speed
and which results in an increase in the effective diameter of a disc, measurements of
which are given in Section 16. The wire for the phosphor-bronze segments is 25 sq. mm.
in cross section and was kindly drawn for us by the London Electric Wire Company.
Some of it was further drawn down into circular section wire of 0*12 mm. diameter,
and this latter was employed for the brushes. Phosphor bronze was chosen for the
segments and brushes because of the negligible tendency to bind and tear when this
alloy is employed for moving parts in contact.

Fig. 5.

Fig. 5 shows five segments in position on a disc and illustrates the manner in which
the wires pass from the segments to the main shaft. Before making any resistance
measurements the shaft was rotated slowly, and with the aid of a small portable
milling machine a smooth surface was turned on the segments. The sharp edges
which resulted at e, e (fig. 5) were rounded in order to avoid a cutting action on the
wire brushes.

Section 7. — The Brushes and Their Lubrication.

To obtain experience regarding the best form and number of brushes, preliminary
apparatus consisting of two rotating discs of phosphor bronze was constructed in 1908.

RESISTANCE BY A METHOD BASED ON THAT OF LORENZ. 43

The apparatus was astatic and our experiments were directed to eliminating trouble
due to thermo-electric effects at the brush contacts.

The first brushes experimented with were of fine phosphor-bronze wire, each brush
consisting of about 50 wires bound together after the manner of a common pencil
brush. A light spiral spring ensured contact between a brush and the edge of a disc.
A circuit through brushes, discs, and a galvanometer was completed, and the discs
(25 cm, in diameter) were run at a speed of about 1500 revolutions per minute.
Whatever thermo-electric effects existed at the points of contact of the brushes
on one disc must have been in opposition to those at the brush contacts on the
other disc, but the galvanometer deflection was far from steady, the variations in the
thermo-electric effects amounting to about 0*0001 volt. Although these preliminary-
experiments of ours were so unsatisfactory, the results were much better than those
obtained when the circuit was completed through brush contacts at the edge of one
disc and others on the shaft of the apparatus.

An even more disturbing feature of our experiments was the inconstancy of the
resistance of the galvanometer circuit. With one brush on each disc the resistance of
the contacts was measured as something less than 01 ohm when the discs were
stationary, but when the discs were rotating the contact resistance increased to 5, 10
and 20 ohms, and at times the circuit appeared to be broken. This effect was
undoubtedly due to a vibration of the brushes brought about by the motion of the air
at the edges of the discs. In practice it was not possible to prevent this by increasing
the pressure applied to a brush, as by doing so the discs were worn away very rapidly
and the points of contact became very hot. Shielding devices were tried with some
small success, but the most favourable results were obtained by employing a number
of brushes in parallel and placing in series with each brush a resistance of 1 ohms,
thus ensuring that any increase or diminution of the resistance of one brush contact
would have but little effect on the circuit as a whole. Our experimental results
showed clearly that the employment of a large number of brushes was beneficial, but
an increase in the number did not greatly improve the results, unless a resistance was
placed in series with each before the brushes associated with any one disc were placed
in parallel.

A further advance was made by lubricating the edges of the discs. Fatty oils and
greases are impossible for such a purpose as the contact resistances are enormously
increased and the general result is far worse than when no lubricant at all is used.
Acheson graphite, aquadag and oildag were tried, but the results were not satis-
factory. It is not very well known that paraffin oil improves all ordinary contacts
such as those associated with slide wires, plugs, &c, but throughout the National
Physical Laboratory paraffin oil is largely used for such purposes. We tried it there-
fore as a lubricant for the brushes. There was a marked improvement in the results,
and we continued to use it in this preliminary work. Many kinds of brushes were
tried : some were wires of phosphor bronze, some of phosphor-bronze gauze, some of

G 2

44

MR* F. E. SMITH ON THE ABSOLUTE MEASUREMENTS OF A

copper wire, and solid slipper brushes of phosphor bronze were also used. The most
satisfactory results were obtained with brushes of fine wire.

After the erection of the Lorenz apparatus we continued our experiments with
brushes. The discs of the new apparatus are about 53 cm. in diameter and they
revolve about 1050 times per minute, so that the velocity at the edge of a disc is
about 1750 m. or 1 mile per minute. This velocity is greater than the velocity at
the edges of the discs in our preliminary apparatus, and we found the brush difficulties
correspondingly increased. The variation in the resistance of the galvanometer
circuit due to the varying contact resistances rendered accurate work impossible, and
we were led to design a brush which would not be set in vibration except to a very
small extent and by the use of which thermo-electric effects would produce compara-
tively small disturbances. A short description of these brushes appeared in the
'Annual Eeport of the National Physical Laboratory for 1911/ and we are aware
that the short description there published has led several investigators to try similar
brushes, and the results have been reported as satisfactory.

We were guided in the design by the following considerations : ( 1 ) a fine cylindrical
wire if stretched offers little resistance to a stream of air, and whatever vibration is
set up will probably be regular and can be controlled by adjustment of the tension on
the wire ; (2) if a wire such as AB (fig. 6) is in tension and makes contact with the

Fig. 6.

edge of a rotating disc D over the arc EOF, the pressure will be greatest at a point
close to C the mid-point, and will gradually fall in value until at E and F it is zero.
The maximum rise of temperature and the maximum thermo-electric effect will
probably be at 0, and the thermo-electric force will gradually diminish as we approach
E and F and be zero at these points. Without the completion of any other circuit it
is clear that electric currents will be produced which will flow from the wire to the
disc in some parts and from the disc to the wire in other parts. If, therefore, a
galvanometer is included in the circuit containing the junction of wire and disc, the
resultant deflection will be very much less than that which would be produced by the
maximum thermo-electric effect. A number of stretched wires in parallel should, of
course, give better results than one. The form of brush actually used in our
experiments is depicted in fig. 6. The size was largely governed by the arc of contact
desired and the number of segments on the discs.

KESISTANCE BY A METHOD BASED ON THAT OF LOEENZ. 45

The brushes are of phosphor-bronze wire 0*12 mm. in diameter, and to obtain as
small a thermo-electric effect at the contacts as possible the wire was drawn from
other wire of square section similar to that employed for the segments on the discs.
To make a brush, the fine wire is wound in screw cut grooves of 0*25 mm. pitch, cut
on small brass cylinders which can rotate about, or be clamped to, the axles AA'.
The ends of the wire are soldered to the cylinders and the wire brush thus formed is
put in tension by operating the milled heads HH. The spiral springs SS' are of stout
phosphor-bronze wire and are soldered to brass rods RR/, of square section, which
slide in square cut grooves cut in the frame F. The overall length of a brush is
20 cm. In practice we found the tension required for good working to be very small ;
a tension corresponding to the pull produced by the suspension of a 200 gr. weight
was found to be most satisfactory. Some of the brushes were made with eight
turns of wire, some with three turns, and a few with one turn ; the majority were of
three turns.

From the moment we commenced to use this style of brush with petrol as a
lubricant, the thermo-electric variations produced very much less trouble. The
variations are not more than one-fiftieth of those found with any other form of brush
we have experimented with, and the variation in the resistance of the contacts when
ten brushes are placed in series is so small that the sensitiveness of the galvanometer
remains constant within the limits of error of our measurements. However, in the
case of ten brushes in series, the tension on the wires has been somewhat greater than
that recorded above.

Without a lubricant the brushes are not satisfactory. The wire is gripped by the
disc and under certain conditions the brushes vibrate longitudinally and produce at
the same time a chattering noise. Also the wire and disc become rugged and the
temperature at the point of contact is very much greater than when petrol is used as
a lubricant. We believe the petrol to have three beneficial influences : (l) as a
lubricant ; (2) as a cooling agent ; (3) as a cleanser getting rid of all traces of grease and
dirt. The amount of petrol to be supplied and the manner of supply was the subject of
many experiments, but it is sufficient to state here the manner eventually adopted.

Fig. 5 shows a brush in position and a petrol supply vessel V. The brush is
secured to a massive phosphor-bronze ring R (see figs. 3 and 5) by the screws SS',
and it can be placed in contact with a segment or removed from such contact by
loosening the terminal head H and giving the brush frame a circular motion about the
pivot screw S'. The screws SS 7 and the brass distance pieces BB 7 are insulated from
the ring R by means of ebonite sleeves, the latter allowing of some adjustment of the
screws SS'. The ring R is supported by the bed B (fig. 4) but is insulated from it.
Stretched phosphor-bronze wires support the ring laterally and give it the necessary
rigidity.

The petrol supply vessel is of glass, the tube being drawn down to a capillary about
0*5 mm. in diameter at its lower end. On the narrow glass tube thus formed, a

46 MR. F. E. SMITH ON THE ABSOLUTE MEASUREMENTS OF A

piece of circular lamp wick about 3 cm. long is slipped ; the lower end of this wick
just touches the rotating segments and thus feeds petrol directly on to the surface of
the segments. The usual rate of supply of petrol was about 500 c.c. in twenty
minutes. When the apparatus is running well, an observer may place the end of a
finger on the rotating segments and find it well flooded with petrol removed from the
rim. The wicks are renewed at least every day and the brushes wiped with clean
chamois leather. In our experiments a set of ten brushes lasted usually for six or
nine complete sets of observations ; after that number the surfaces of the wires
became somewhat rough and the results were not quite so satisfactory. The
magnitude of the changes of the thermo-electric effects with two sets of five brushes
in parallel will be realized when it is said that often for intervals of twenty minutes
the rapid variations in the total thermo-electric voltage did not exceed 0*1 microvolt.
A slow progressive variation was commonly observed, but this was not a source of
trouble.

Section 8.— The Coil Supports.

Each marble cylinder weighs about 50 kgr. and is supported on a phosphor-bronze
cradle C (fig. 4) so that its axis is coincident with the axis of the shaft. The base of
the support is a triangular casting G, which is supported in turn by three levelling
screws A on the " hole, slot, and plane " principle. The pitch of the levelling screws
is one millimetre and the heads of the screws are divided into one hundred equal
divisions, thus enabling any particular vertical motion to be repeated within one-
hundredth of a millimetre.

A second triangular casting K carries the levelling screws and is fitted over a large
central stud attached to a slide, so that the cylinder may be rotated about a vertical
axis if necessary. The maximum angular motion is 12 degrees and the magnitude of
any motion can be directly read on the engraved head of the horizontal screw E to
half a minute of arc. Backlash is avoided by the use of strong phosphor-bronze
springs.

A cylinder and the cradle supporting it can be moved 5 cm. in two horizontal
directions at right angles by means of two slides, the motions being controlled by screws,
the heads H of which are divided to read hundredths of a millimetre as in the case of
the screws for the vertical motion. For these movements also strong phosphor-bronze
springs are employed to prevent backlash.

Section 9. — Lubrication of Bearings.

The bearings of the machine are nine in number, each of those of the motor being
about 9 cm. long and each of the remaining seven about 14'5 cm. long. The lubricant
used is best turbine oil which is fed to the bearings under a pressure of about
15 lbs. per square inch, the rate of supply being a cubic foot of oil every five minutes.
The oil supply tank and pump are of phosphor bronze and are situated under the

RESISTANCE BY A METHOD BASED ON THAT OF LORENZ. 47

floor, l|- m. below the level of the bearings of the main shaft, and 4 m. distant
from the nearest point of the machine. The pump is driven by a small motor of one-
eighth horse-power and forces the oil through copper pipes to the bearings of the
machine. After passing through the bearings the oil returns through copper drain
pipes to the tank and is strained through fine copper gauze before again entering the
pump. The system works excellently, no trouble whatever having been experienced.

Section 10. — Regulation of Speed.

On the axle of the motor a commutator is fitted which serves to charge and discharge
a condenser four times for each revolution of the shaft. The condenser is placed in
one arm of a Wheatstone bridge, the other arms of which are platinum-silver resistance
coils. Balance of the bridge results for a particular frequency only of charge and
discharge, and to maintain a balance over a considerable length of time the frequency
and therefore the speed of the Lorenz apparatus must be kept constant. To ensure
constancy of the arms of the bridge, the condenser and the platinum- silver resistances
were kept in a constant temperature room ; a small variable resistance in series with
one of the arms was in general adjusted to secure a balance when the speed was that
best suited for the resistance measurements, but after the latter measurements had
commenced the speed only was controlled to maintain the balance. The galvanometer
used was a suspended coil instrument, the spot from which was received on a ground
glass scale mounted over the fly-wheel ; an assistant observer, S. Watts, applied a
variable pressure to the fly-wheel and so maintained the balance of the bridge. A
change in the speed of the Lorenz apparatus of 1 part in 10,000 produced a deflection
of the galvanometer spot of 4 mm., and in general, a balance was maintained for twenty
minutes or more with a maximum deflection not greater than 2 mm. ; occasionally,
better results than this were obtained. An adjustable resistance is in series with the
field coils of the motor, and before attempting to govern the speed this resistance is
altered until a speed results which is very slightly greater than that desired.

The motor was run from a battery of large storage cells and very good results were
obtained with no regulation at all, if the current flowed sufficiently long (generally
from one to two hours) to raise the field coils to an approximately constant tempe-
rature. However, the method finally adopted enabled resistance measurements to be
made a few minutes after starting the motor. A somewhat similar method of
controlling speed for measurements of capacity has been in use for several years both
at the National Physical Laboratory and at the Bureau of Standards.

Section 1 1 . — Method oe Recording the Speed.

The chronograph described is very similar to one designed at the Bureau of
Standards, # and made by the Societe Genevoise, for details of which the writer

* i

Bull. Bureau of Standards/ vol. 3, p. 561.

48 ME. F. E. SMITH ON THE ABSOLUTE MEASUKEMENTS OF A

is indebted to Dr. Rosa and other members of the Bureau of Standards. The
instrument described below, which is of brass, was made by Mr. Mubfitt of the
Instrument Department of the Laboratory.

The method of recording the speed is a direct one. A chronograph drum is geared
to the main shaft of the apparatus through the medium of two worm wheels and two
spur wheels, the gear ratio being 174. The usual speed of the main apparatus is
about 1044 per minute, and under such conditions the drum of the chronograph makes
one revolution in ten seconds. An electro-magnet is supported on a carriage which is
connected to a split-nut engaging with a screw of 1 mm. pitch. The direction of
travel of the carriage is parallel to the axis of the drum and it advances 1 mm. for
each revolution of the drum. Every second a current passes through the electro-
magnet and the latter operates a small punch, which, striking through a typewriting
ribbon, prints a dot on a sheet of paper carried by the drum. The circumference of
the drum is exactly 500 mm., so that when six revolutions per minute are made,
successively recorded dots are 50 mm. apart. The split-nut fixed to the carriage
carrying the electro-magnet can be disengaged from the driving screw and the carriage
rapidly run along the rails supporting it. When the printing punch is pressed
forward during this operation a line parallel to the direction of travel of the electro-
magnet is printed on the paper. This line is hereafter called the base line and by
measuring the angle between it and a row of dots recorded during a run, the speed
can be calculated, with great accuracy.

The method of calculating the speed is as follows : At a speed of exactly 1044
revolutions per minute there are 1044/174 = 6'0000 revolutions of the chronograph
drum per minute. The resulting record will therefore be ten rows of dots, the dots
being 1 mm. apart, and the rows 50 mm. apart and parallel to the base line. If the
speed is slightly diminished or increased, the rows of dots will slope upwards or
downwards. In practice, a set of observations for the measurement of a resistance is
made to last for at least 1000 seconds (i.e., about 17 minutes), and the resulting rows
of dots are therefore more than 10 cm. long. From a portion of the base line lying
beneath (or above) a row of dots a length of 10 cm. is marked off, and from the
extremities of the 1 cm. line ordinates are drawn to the nearest row of dots. If these
ordinates are equal in length the rows are parallel to the base line, and the distance
between two dots recording an interval of 1000 seconds (10 cm. run) is 50,000 mm. if
the distance is measured along the trail of the recorded seconds. If the ordinates are
not equal in length the machine was running either faster or slower than 1044
revolutions per minute ; which of these holds good is decided by the direction of the
slope. Suppose the difference between the ordinates is 14*5 mm. and that the machine
was running faster than 1044 per minute. The mean speed is calculated to be

1044 x = 1044'30o revolutions per minute. It is clear that a difference

50,000-14-5 F

between the ordinates of half a millimetre corresponds to 1 part in 100,000 of the

RESISTANCE BY A METHOD BASED ON THAT OF LORENZ. 49

speed. The drum is 50 cm. long and a record lasting 80 minutes can therefore

Fig. 7 is a full-size reproduction of a portion of a record, taken June 26, 1913. The
recorded speed is 1043'96 2 revolutions per minute. The rows of dots enable the mean
speed to be calculated with an error certainly not greater than 1 part in 100,000, and
the speed throughout (as illustrated by the rows of dots lying in a straight line and
not a wavy one) is wonderfully uniform. The general fluctuations of speed cannot
be detected on the record, but their magnitude has been estimated in another way as
explained in Section 23.

A mercury contact is used on the pendulum of the standard clock and a relay is
operated continuously by the current which passes. The rate of the clock is of course
allowed for.

Section 12. — Magnetic Tests.

Magnetic tests were made on all the materials employed. With the exception of
the motor, we are satisfied that the permeability of no part of the machine and the
concrete bed on which it rests differs from unity by more than 2 parts in 100,000.

Every part of the machine bears a distinctive number. When each part was cast,
a lug about 5 cm. long and 5 cm. in diameter was cast with it, and after being stamped
with the same number as the casting it was forwarded by Sir W. G. Armstrong,
Whitworth & Co. to be tested for magnetic quality. In the case of springs, rods,
tubes, &c, pieces were cut from these and used for the tests.

The method of testing was similar to that employed for the parts of the current
balance. # Soft iron wire and ferrous sulphate were used to calibrate the apparatus
and sufficient sensitiveness was obtained to detect a difference from unit permeability
of about 1 part in 100,000. Thus, when powdered ferrous sulphate having a
permeability of about 1*00044 was contained in a glass tube having the same cross
section as most of the test pieces, the resulting galvanometer deflection was 5*2 mm.
The test pieces of marble were of much larger cross section than the glass tube and
the sensitiveness was correspondingly increased.

Trouble was experienced with a number of brass rods and tubes and with the shaft

of the apparatus. The first shaft was made of phosphor bronze and had a magnetic

permeability of 1*006 ; in consequence this shaft was rejected. The material obtained

for the second shaft was of an alloy of copper and aluminium (copper 90 per cent.,

aluminium 10 per cent.) and was also rejected as its permeability was about 1*002.

The third shaft was made with specially pure aluminium and copper in the same

proportions as before, and its permeability differs from that of air by an amount too

small to be detected. The billet for the shaft was prepared by The Broughton Copper

Company, Limited, of Manchester, and we thank them for the care taken in its

preparation.

* 'Phil. Trans/ A, vol. 207, p. 475, 1908.

VOL. CCXIV.— A. H

50 ME. F. E. SMITH ON THE ABSOLUTE MEASUREMENTS OF A

*£*•«%«• *««»f«*«tt»*«t*«tt+94******«e«t

•••••"•••—♦•* •'•"••••"••••"•••••••••MMtMM«-..M«*M,»«M.,

*••" ' "•♦••• * " ' ••••..,., ....... .•».«.,«»»«••,

Base Line.

Fig. 7.

EESISTANCE BY A METHOD BASED ON THAT OF LORENZ. 51

The samples of Portland cement tested varied in magnetic permeability from 1*0005
to 1*0020. It is possible that metallic iron finds its way into the cement from the
steel grinding machines, and the Associated Portland Cement Manufacturers very
kindly offered to exclude such contamination by grinding some cement through mill-
stones. At the same time the manufacturers pointed out that a certain amount of oxide
of iron in combination with lime and silica is invariably present in Portland cement,
and Keene's cement was suggested as being suitable for our purpose. This is a
white cement absolutely free from iron compounds of any sort. We tested several
samples for magnetic quality, and finding it quite satisfactory decided to use it for
the block on which the apparatus rests. No trouble was experienced in obtaining
sand and ballast free from magnetic substances.

Section 13. — Construction and Measurement of the Coils.

" First Statuary " Carrara marble was chosen for the material of the cylinders. We
were guided in our choice by our experience with the cylinders for the Ayrton- Jones
current balance, the tests then made showing marble to be an excellent electrical
insulator and of negligible magnetic susceptibility.

The cylinders were prepared in the rough by Messrs Walton, Gooddy & Cripps, whom
we thank for the trouble they took in choosing masses of marble practically free from
veins. The small shiny specks which are often present in Carrara marble consist of
iron pyrites which has a magnetic susceptibility of about 0*0005. The conductivity
of iron pyrites is much greater than that of marble and any small specks on the
surface of a cylinder should therefore be removed ; we found that a small crystal of
pyrites pressed between two plates of copper reduced the insulation between the
plates from a value which was practically infinity to 1000 ohms. Clearly a large
number of crystals at the surface of a marble cylinder would introduce a serious source
of error.

The coefficient of expansion of the marble was determined by direct measurements
on the cylinders and found to be 5*0 x 10~ 6 for 1° C, the temperature range being
from 11° C. to 20° C. These measurements are described in the section dealing with
the measurements of the mean diameters of the coils.

The cylinders chosen are free from flaws and cavities. Of six cylinders which were
submitted, two exhibited " ground flaws " and were in consequence rejected. These
"ground flaws" appear to have been produced by a rupture in the marble many
thousands of years ago and subsequent re-union by pressure or equivalent agency.
In all, Messrs Walton, Gooddy & Cripps prepared 16 cylinders in the rough and the
four best of them were chosen for our work.

The marble cylinders for the Ayrton-Jones current balance were baked in an oven
at 140° C. for 30 hours and afterwards immersed in hot paraffin wax. At the same
time a marble rod was subjected to similar treatment, and since that time this rod has

H 2

52

MR. F. E. SMITH ON THE ABSOLUTE MEASUREMENTS OF A

been kept under observation in the Metrology Department. Possibly there is a flaw
in the rod, but it is certain its length has not kept so constant as other rods which
were not baked and immersed in wax. We decided, therefore, to omit the treatment
in the case of the four cylinders for the Lorenz apparatus.

The cylinders were turned in a manner very similar to that employed for the
suspended coils of the current balance. The inner and end surfaces of a cylinder
were turned with the cylinder fixed to the face plate of the lathe, but the outer
surfaces and double spiral grooves were cut when the cylinder was mounted on a
specially constructed mandrel supported between dead centres. The inner and outer
surfaces of a cylinder are practically concentric and the ends at right angles to the

axis.

The turning of each cylinder occupied about four weeks. The cylinders referred
to as Nos. 1 and 2 were turned by the late Mr. Taylerson of the Engineering
Department of the Laboratory. Mr. Taylerson had marked ability for accurate
work of this kind and made many useful suggestions during the progress of the work.
The turning of cylinders Nos. 3 and 4 was very ably done by Mr. Tribe of the
Engineering Department.

The winding of the coils was carried out in a manner identical with that employed
for the coils of the current balance. It is only necessary to state here that the coils
were wound with the wire in tension, the effective load on the wire during winding
being 4 kgr. The cylinders were rotated very slowly and after each revolution a
stoppage was made for measurements to be taken of the diameter of the wire.

The leads of all the coils must lie in a plane containing the axis of the cylinder, for
otherwise the mutual inductance of the leads and the discs will not be zero. To

ensure the absence of any correction due to such

a cause, the connections to the coils were made in

the manner shown in fig. 8. At the points where

the coils terminate, two radial cylindrical holes

a and b are drilled and enlarged to admit of the

slotted brass nipples NN 7 being screwed into

them. Soldered connections are made between

the nipples NN', the leads c and d y and the leads

through a and b. The leads c and d pass to two

brass blocks mounted on an ebonite piece screwed

to one end of the cylinder, and to these same

blocks a small concentric cable is secured in the manner illustrated in the figure. The

whole of the leads r shown in the figure lie in an axial plane of the coil and this same

plane contains the leads connected to the other coil on the cylinder.

An estimate was made of the accuracy with which the number of turns is known.
On each cylinder there are two coils each having 96 turns and a diameter of about
36 cm. ; the length of wire to each coil is, therefore, about 108 m. From observations

N

^v^ a K\x

\\\\\\\n\\\\n

\7

Fig. 8.

RESISTANCE BY A METHOD BASED ON THAT OF LORENZ. 53

on the radial holes and a consideration of the methods adopted for drilling them, the
number of turns is considered to be correct within 2 parts in 1,000,000.

The copper wire with which the eight coils are wound was supplied by The London
Electric Wire Company on bobbins of the same diameter as the cylinders. It is hard
drawn No. 24 S.W.G. and its mean diameter, obtained from about 800 measurements
taken when winding the coils, is 0"557 5 mm. The diameter was also measured in the
machine employed to determine the diameter of the coils, the mean of eighty measure-
ments being identical with that already given.

Measurement of the Mean Diameters of the Coils.

Twelve axial planes at angular distances of 1 5 degrees apart are marked on the end
faces and on the ungrooved portions of the outer cylindrical surfaces of each cylinder.
These planes are numbered 1 to 12 and are the reference planes in the diametral
measurements. Each cylinder was mounted in turn on the mandrel employed for
turning the outer surfaces and supported between dead centres attached to the
measuring machine.

This machine was made by Sir W. G. Armstrong, Whitworth & Co. at their Openshaw
Works, to designs prepared by the firm in collaboration with Mr. L. F. Richardson,
formerly of the Metrology Division of the Laboratory. It consists of a straight bed
carrying two fixed headstocks with cone-centres, between which the coil, on its
mandrel, can be mounted. A saddle sliding on the bed carries two measuring head-
stocks on a slide which is adjustable so as to bring the line of centres of these head-
stocks exactly perpendicular to that of the fixed headstocks. Each of the measuring
headstocks contains a barrel which can be moved in and out along the line of centres
by means of a carefully calibrated micrometer screw ; and sliding freely in the centre
of each barrel is a plunger, the front end of which constitutes the measuring face,
while the rear end carries a small knife-edge pressing against a vertical lever
pivoted in the barrel. At its upper end this lever carries a sensitive spirit
level. The barrel is advanced by means of the micrometer screw until the
plunger, being arrested by contact with the object to be measured, tilts the level
far enough to bring the bubble to a definite mark. The reading is then taken
with the aid of a vernier on the measuring wheel attached to the micrometer screw,
to 100 * 000 inch. The same operation is carried out with each of the two measuring
headstocks, one at either end of a diameter, and the sum of the readings is compared
with the sum of similar readings on a gauge bar of known length. For convenience,
this gauge bar is mounted on the machine during the measurements, so that by simply
traversing the saddle from the coil to the gauge the zero reading can be checked at
any stage of the work. To provide for this, one of the cone centres is made specially
large, and pierced behind the cone by a hole through which the gauge can be passed.

In the original design the control of the vertical lever carrying the level was effected

54

ME. F. E. SMITH ON THE ABSOLUTE MEASUREMENTS OF A

by means of coiled springs contained in the barrel. It was found, however, that this
arrangement gave rise to a greater pressure than was desirable at the point of contact
between the plunger and the coil. Owing to the small radius of the wire with which
the coils are wound, a comparatively slight pressure would produce deformation
sufficient to lead to errors in the readings. A calculation showed that in order to
keep errors due to this cause within allowable limits (less than x^o o mm - on "the
diameter) the pressure must not exceed four or five ounces. At the suggestion of
Mr. J. E. Sears, the springs were taken out and the vertical lever was extended
downwards and provided with a weight at its lower end, thus forming it into a
pendulum with a gravity control which could be adjusted to a nicety, At the same
time the form of the body of the plunger was slightly modified, and its bearing
surfaces lightly polished, so as to minimize friction. In this way the contact pressure
was reduced to within the required limits.

Many measurements of the coils were made with a current passing through them
in order to reproduce as nearly as possible the conditions under which they would
actually be used. To enable this to be done, the plungers were provided with non-
conducting measuring faces of polished agate. These proved highly satisfactory in
use, and the measurements made with the machine were of quite remarkable
accuracy.

Two pairs of Hartmann steel gauges were employed in the measurements. The
following table gives their values at 0° C. : —

Table II. — Giving the Values of the Gauges employed.

#

Approximate length of
gauge in millimetres.

Gauges 300+ 60
200 + 160

Sevres value.

-

N.P.L. determination,

using the Sevres value of

the 1000 mm. gauge

as basis.

mm. fji

60-1-5

160-0*7

200 + 0-1

300-1-1

mm. /x
60-1-3
160-0-7
200 + 0*4
300-0-9

Sevres value.
mm. /*

360-2*6

360-0-6

N.P.L. value,
mm. /x

360-2-2

360-0*3

The Sfrvres values are stated to be accurate within 0'5/x, and the probable error of

* fi = 1 micron = 0*001 mm.

RESISTANCE BY A METHOD BASED ON THAT OF LOEENZ.

55

the N.P.L. values is of the same order. By taking the means of Sevres and N.P.L.
determinations as the best obtainable, we have

300+. 60 == 360 mm.-2 , 4/x at 0° C.,
200 + 160 = 360 mm.-O'4/x at 0° C.

Using the dilatation equation determined at Sfevres on a bar of the same material

L, = Lo {1 + (10*469 + 0-00358*) t x 10~ 6 }
we get the following lengths at 17° O. : —

Gauges (300+ 60) = 360*062 mm.,
(200 + 160) = 360'064 mm.,

with an increase of 3"8/a on the 360 mm. length per 1° C. increase in temperature at

To obtain the mean temperature of the marble, holes were drilled in the cylinders
and in these holes thermometers were inserted. The holes are parallel to the axis of
the coils, and the depth of each is about half the axial length of a cylinder, so that
the temperature recorded by a thermometer is very approximately the mean
temperature of the cylinder.

The temperature coefficient of expansion of the marble was determined by making
diametral measurements at temperatures varying from 11° C. to 20° C. Assuming
that the coefficient of expansion of the steel
gauges is correct, the mean coefficient of linear
expansion of the marble was found to be
51 xl0~ 6 for the range 11° C. to 20° C. The
observations were remarkably consistent, as will
be seen from fig. 9, in which the difference of
expansion of the steel and marble is plotted
against temperature. During these observa-
tions we were much struck with the compara-
tive rapidity with which the temperature of the
marble followed that of its surroundings. The
temperature coefficient of expansion of the
marble was also deduced from measurements
of the axial length of a cylinder. In this case
the difference of expansion of invar and marble was directly recorded, and taking the
invar as known the value obtained for marble is 4*9 x 10~ 6 , which is in good agreement
with the value given above. When required in our work we took the mean of
these values, i.e., 5*0 x 10~ 6 , as correct.

As already stated, the contact pieces of the measuring machine are of agate, in

20jx

5

u

fO

z

o

z

</)

z

i

X

fO

I

, , — i— _ .- — - —+/C — . - ,....._,, ■__ — ■ - ■. — — —

_f 1 , ______ — „.., ., ..,. ■— — ■ — _ —■ ..■■->■■ 1

I2L

TEMPERATURE

20

22

Fig. 9. Differential expansion, steel-marble.

56

ME. P. E. SMITH ON THE ABSOLUTE MEASUREMENTS OF A

order that measurements of diameters may be made while a current is passing
through the coils. The current used in our absolute measurements of a resistance
did not exceed 2 amperes, and we experimented with such a current through the
coils during our measurements of the diameters. Preliminary observations showed
that the expansion of a cylinder 5 minutes after switching on the current was
sufficiently great to allow of a definite measurement being made, and a thermometer
recorded an increase of temperature of a whole degree in this time. A survey of the
surface of the coil showed the expansion to be greatest in the mean diametral plane,
and least at the ends ; measurements were, therefore, made on four turns of wire,
these being the 1st, 16th, 48th, and 96th strands measured from one end.

<

u.

o

u

<

2

10

20

30

40 SO SO

TIME IN MINUTES

80

Fig. 10. Showing increase in temperature of marble cylinder and increase in diameter of certain parts of

the coils when a current of 2 amperes is passed through them for 37 minutes.

indicates temperature observations

x

t

observations on strand No. 96

48

J5

JJ

5J

JJ

r

16
1

measured from one end of coil.

The results of the measurements are given in figs. 10 and 11. In fig. 11 the
expansion of the coil is given 5, 10, 15, 20, 25, and 35 minutes after a current of
2 amperes was switched on. The maximum increase in diameter is 10*4^. Fig. 10
shows the rise in temperature recorded by the thermometer when the current was
left on for 37 minutes, and shows also the fall in temperature after the circuit was
broken. A relation between the mean rise in temperature due to the current and

EESISTANCE BY A METHOD BASED ON THAT OF LOBENZ.

57

the change in mutual inductance of the coils and the discs was worked out and found
to be extremely useful when making the resistance measurements. The relation is
as follows: — " If, in the resistance measurements, t x is the mean of the initial
temperatures of the marble cylinders, and t 2 the mean of the final temperatures, the
mean mutual inductance (during the resistance observations) of all the coils and the
two discs is the same as when the temperature of the cylinders is uniform throughout
and equal to ^ + 0*42 (* 3 — other things being kept constant."

END

CENTRE

END

Fig. 11. Showing expansion of coils on marble cylinders at intervals from 5 to 35 minutes, when a

current of 2 amperes is passed through them.

Complete measurements of the coils have been made on three occasions. The first
set of measurements was made in February and March, 1912, and two sets were
made in April, 1913. In the first set 192 observations were made on each coil, 16
observations being made in each of 12 axial planes 15 degrees apart. The turns of
wire measured in any one plane were 1 cm. apart, and neighbouring strands were
measured in succeeding planes, so that one measurement was made on every turn

of wire.

In the measurements made in 1913, six measurements were made in each of 16
diametral planes 1 cm. apart, alternate sets of six measurements being made in axial
planes 30 degrees apart, and the remaining measurements were made in planes
midway between these. In addition, 16 observations were made in each of three
axial planes 60 degrees apart, thus making 144 observations in all. Both pairs of
gauge bars were used, and the difference found between them is identical within 0'5/>c
with that deduced from the values already given.

In the following table we give the mean diameters of the coils on the four cylinders
as deduced from the measurements made in February and March, 1912, and April,
1913 :—

VOL. COXIV. — -A. I

58

ME. E. E. SMITH ON THE ABSOLUTE MEASUREMENTS OF A

Table III. — Giving the Mean Diameters of the Coils at 20°'0 C.

Coil on cylinder

No.

February-March,
1912.

April, 1913.

Mean.

(a)

0)

1

2
3
4

cm.

35-8808 3
35-8817 6
35-8855 4
35-88674

cm.
35-8807 2
35-8815 2
35-8853
35- 8866 2

cm.
35-8806 8
35-8815
35-8853 4
35-88644

cm.
35-8807 4
35-8815
35-8853 9
35-8866

The values recorded in columns 2 and 3 are exactly the means of 192 and 102
measurements respectively. The values in column 4 are not quite the means of the
48 observations. The cylinders are not quite circular in cross-section, and the mean
of 48 measurements in three planes should, in general, be different from the mean of

Table IV. — Giving the Results of Measurements of the Diameters of the Coils on

Cylinder No. 1. Temperature 20°'0 C.

Axial plane No. . .

1

2

3

4

5

6

7

8

9

10

11

12

Measurements on
turn No.

Diameter = 35 • 8750 cm. +

Mean.

fi.

p.

/*•

/x.

[i.

/*•

/x.

/x.

jjb.

[A.

p.

p.

fi.

1

29

14

22

27

30

30

25-3

12

27

26

31

36

36

23

29- 8

24

34

30

32

36

35

35

33>

36

35

37

42

41

47

45

41- 2

48

41

39

39

46

48

49

43 - 7

60

40

42

48

47

49

48

45- 7

72

61

57

59

61

64

63

60- 8

84

65

66

69

70

75

65

68- 3

96

67

65

76

74

72

70

70- 7

108

70

69

72

69

78

66

70- 7

120

58

61

63

65

72

66

64- 2

132

66

65

73

74

73

68

69-8

144

67

63

68

69

71

72

68- 3

156

66

70

74

76

70

73

71-5

168

75

67

73

71

72

71

71-5

180

65

67

70

72

65

66

67-5

192
Mean . „ . =

64

65

70

74

78

70

70-2

55-!

53- 9

51- 2

55- 2

55- 8

59- 9

58-x

60- 6

60-3

61- 6

58-4

56- 8

57- 2

.\ Mean diameter (centre to centre of wires) = 35-8750 + 0*0057 2 = 35*8807 2 cm. at 20° -0 C.

RESISTANCE BY A METHOD BASED ON THAT OF LOEENZ.

59

measurements made in a large number of planes. This difference can be obtained
from curves showing the cross-section of the cylinders, and in all cases we have
estimated this difference and applied a correction.

It will be observed that the means of the 1913 measurements are about 2/a less
than those of 1912. This difference cannot be due to the gauge bars employed, and
we believe it is not due to errors of observation ; it is probably due to a real

Table V. — Giving the Results of the Individual Measurements on the same Coils,

when Measurements were made in Three Planes only.

Axial plane No. . .

Between 3 and 4

Between 7 and 8

Between 11 and 12

Measurements on
strand No.

Diameter = 35 • 8750 cm.

+

Mean.

■ Y

/x.

/x.

fi.

li.

2

24

28

31

27'r

12

24

29

32

28- 8

24

26

32

35

31-o

36

32

35

38

35-o

48

40

42

47

43-o

60

42

45

47

44- r

72

54

66

65

61>

84

61

66

67

64>

96

58

61

69

62- r

108

67

71

74

70>

120

57

69

63

63-o

132

61

67

67

65-o

144

56

75

70

67-o

156

71

79

76

75-3

168

67

80

74

73>

180

68

75

71

71*3

192
Mean . . . =

70

79

75

74- 7

51*6

58-5

58- 9

56-3

.\ Mean diameter - 35 -8750 + 56*3/* = 35«8806 3 cm. at 20° *0 C.

From fig. 12 and the observations in Table IV. we conclude that the mean diameter in these three
planes is less than that of the complete coils by 0*5/x. Hence mean diameter of the coils = 35*8806 8 cm.
at 20° -0 0.

diminution in the diameters of the coils due to a displacement of small crystals of
marble under the wires. This is quite possible, as the coils are wound under tension
and have been subjected to considerable changes in temperature (due to the current
passing through them) since 1912.

Tables IV. and V. give the results of the individual measurements made in April,
1913, of the coils on cylinder No. 1.

I 2

60

ME. F. E. SMITH ON THE ABSOLUTE MEASUREMENTS OF A

The curves given in fig. 12 show to what extent the coils vary in diameter. The
conicality of the coils on cylinders 3 and 4 is much less marked than in the case of
those on cylinders 1 and 2, but the variation from a circular cross-section is very
small for all of the coils. The variation of diameter in any cross-section is so small

ao

T

T

j b i H i i >

; > " ■ - ' - f

it==it

4

5 6

9 »0 n 12 i

Fig. 12.

AXIAL PLAN E N°

Showing extent to which coils are conical, and variations in cross-section from circle.

that the mean diameter of the cross- section may be employed for the purposes of the
calculation of the mutual inductance without appreciable error, but the variation in
diameter from end to end of the coils necessitates the application of a conical

correction.

The probable error of the mean diameter of the coils is estimated to be not greater
than 1/x. The probable errors of the gauge bars used are stated on p. 54; the
probable errors of the observations may be estimated from the data given in
Table III.

RESISTANCE BY A METHOD BASED ON THAT OF LOEENZ. 61

Measurement of the Axial Lengths of the Coils and the Variation of Pitch.

The pitch measuring machine, also constructed by Sir W. G. Armstrong, Whitworth
and Co. , consists of a straight horizontal bed provided with dead centres on which the
mandrel carrying the coil can be mounted. Parallel to the line of centres is a slide,
along which a small slide rest can be traversed by means of a calibrated measuring
screw, of T Vinch pitch. The measuring wheel which actuates this screw can be read
to 100 1 000 inch by means of a vernier, but the accuracy of repetition of readings is
somewhat less than this. The slide carries a microscope whose optical axis intersects
the line of centres of the machine at right angles. The microscope is focussed on the
coil and is moved by means of the measuring screw so as to bring the consecutive
turns of the coil, one after the other, into a definite position with respect to the cross
wires in the eye-piece, the reading of the measuring wheel being taken at each setting.
The calibration of the screw is effected by focussing a graduated line standard in the
microscope and taking similar readings on the graduations of the bar. The measuring
screw and slide are themselves movable on a second slide in a direction parallel to the
axis of the microscope, so that by withdrawing them slightly the standard bar can be
inserted at any time between the coil and the microscope, and check readings taken
on it without disturbing the coil

The standard employed was an invar metre, the history of which is so well known
that the probable error over a length of 12 cm. (the axial length of a coil) is less
than I//.

For the measurements on each cylinder, readings on successive half centimetre
divisions of the invar metre were taken over a length of 14 cm., and readings over a
length of 12 cm. (corresponding to the axial length of the coils), were frequently
made. Any change in temperature of the screw of the measuring machine could
thus be allowed for.

As already explained, the two wires on each cylinder are wound in double screw
cut grooves. To measure the mean variation in pitch of the two coils it is better,
therefore, to make observations on the spaces between neighbouring wires than on the
wires themselves, for in the latter case twice as many observations are required. In
practice, observations on the spaces proved the easier way ; the white marble showed
up well between the wires, and it was not difficult to bisect the white spaces by means
of the . cross wires of the microscope. In addition, check observations on the wires
were always ,made. For a complete set of measurements 96 readings are required,
and three such sets in different axial planes were made on each cylinder.

After correcting the readings, the mean pitch of the coils was calculated within a
few parts in 10,000 by dividing the difference of the extreme readings by the number
of turns. The approximate pitch thus obtained was 0*065635 inch (= 0'166712 5 cm.).
We multiplied this number by 1, 2, 3, 4, ..., &c, up to 95, and from the resulting
products the corresponding pitch readings of a coil were subtracted. If the coil had

62

ME. F. E. SMITH ON THE ABSOLUTE MEASUEEMENTS OF A

been perfectly uniform in pitch, the differences would, when plotted, have lain on a
perfectly straight line, but, instead, wavy lines result (fig. 13). As an example of the
difference readings those for the coils on cylinder No. 1 are given in Table VI.

Table VI. — Giving the Difference Readings in Microns for the Coils on

Cylinder No. 1.

fl.

fi.

/x 8

fi.

16

21

36

32

11

20

31

38

7

24

36

37

12

39

47

38

28

43

51

31

31

25

42

35

23

25

36

33

17

19

25

37

5

15

27

37

8

17

35

44

3

30

45

39

23

45

53

43

27

38

40

42

37

31

35

32

27

25

29

38

22

23

23

33

10

26

28

36

12

31

33

41

15

43

45

47

28

50

44

39

46

52

41

36

42

42

34

44

35

40

30

43

28

31

27

37

From the products resulting when the numbers 1, 4, 7, 10, &c, up to 94 were
multiplied by 0*065635, the half centimetre readings for the invar metre were
subtracted and the differences when plotted were found to lie on a straight line as
they should do if all the corrections have been properly applied. The graphs for the
invar metre are shown in fig. 13 and are distinguished as Invar 1? Invar 2 , &c, the
numbers corresponding to the numbering of the four cylinders. A phosphor-bronze
ring is screwed into one end of each cylinder, and these ends are called the " ring ends."

It is clear from fig. 13 that there is a periodic variation in the pitch of all the coils.
The distance corresponding to a complete cycle is half an inch, which is equal to the
pitch of the leading screw of the lathe on which the cylinders were turned. The
cause of the periodicity may be in the leading screw itself, or it may be due to want
of parallelism of the surfaces at which the thrust was taken, or it may be due to both
of these. Such periodic variations in pitch are present in nearly all screws. In
addition to these periodic irregularities, the graphs show others which are taken into
consideration when the mutual inductance is calculated of a coil and disc
circumference.

The graphs for the coils enable one to place the cylinders in pairs. The lengths at

RESISTANCE BY A METHOD BASED ON THAT OF LOEENZ.

63

w

I— I

• r-l
O

o

O
O

• r-l

e!
o

• r-l

c8

*>

a
•in

o

QQ

CO

I-H

&b

• r-l

HOJLId NV3N JO NOIllSOd

tNOdJ 3fclM JO XN3lN30VldSIQ

64

ME. F. E. SMITH ON THE ABSOLUTE MEASUEEMENTS OF A

20° '0 C. of the coils on cylinders Nos. 1 and 2 are 16 '00 18 cm. and 16'0013 5 cm.
respectively; those on cylinders Nos. 3 and 4 are 16*0054 cm. and 16'0054 cm.
respectively. The amplitude of the periodic variation dies away towards one end for
the coils on cylinders Nos. 1 and 2, but for the coils on cylinders Nos. 3 and 4 it does
not. The graphs for the variations in diameter of the coils lend support to this
division of the cylinders into pairs, and as the same lathe and the same portion of the
leading screw were used for the turning of all, the differences appear to be due to a
slight difference in the skill and touch of the late Mr. Taylerson, who turned
cylinders Nos. 1 and 2, and Mr. Tribe, who was responsible for cylinders Nos. 3 and 4.
In all cases the turning is remarkably good.

The mean axial length of the coils on one cylinder is obtained from the graph
showing the periodic variation of the pitch and the corresponding graph for the invar
metre. Limiting our attention to the coils on cylinder No. 1, it is clear that the
extreme mean length of the coils is equal to the length of the invar metre section
AB plus the length corresponding to the difference of the ordinates OA and PB.
The length of the invar section is 15'9996 2 cm. and the difference of the ordinates
corresponds to +17/*. Hence the mean length of the coils on cylinder No. 1 is
15'9996 2 +17m = 16'0013 2 cm. at 14 0, 5 C. = 16*0018 cm. at 20°'0 C.

Table VII. gives the mean axial length of the coils at 20° '0 C.

Table VII.

Coils on cylinder.

Mean axial length at 20° • 0.

1
2
3
4

em.
16-0018
16-0014
16-0054
16-0054

These observations for the mean axial length were made in April, 1913. The
results are identical within the limits of the errors of observation (about 3/x) with
those obtained in March, 1912. A change in the length of a coil of 20^ produces a
change in the mutual inductance of that coil and the two discs of 1 part m 100,000.

Section 14.— Erecting and Adjusting the Instrument.

Before assembling the parts of the machine, a concrete block, built up of Keene's
cement and Thames ballast, was prepared as a foundation. The block is non-magnetic,
is 8 m. long, 80 cm. wide, and 120 cm. deep. Slide rails of gunmetal are bolted in
position on this block and to secure greater stability the rails are sunk 5 cm. into the
concrete. The rails are in three pairs ; one pair support the motor ; a second pair the
fly-wheel ; and the third pair, which are nearly 4 m. long, support the portions with
the rotating discs. A period of twelve months was allowed for the concrete block to

EESISTANCE BY A METHOD BASED ON THAT OF LORENZ. 65

assume approximately constant dimensions, and at the end of that time the upper
surfaces of the rails were scraped to obtain flat surfaces and to ensure these surfaces
lying in the same horizontal plane. Two special fitters from Sir W. G. Armstrong,
Whitworth & Co. carried out this part of the work, and also superintended t|he
alignment of the parts of the machine. The under surfaces of the castings
supporting the fly-wheel, discs, &c, were scraped plane at the Elswick Works and the
alignment of the parts was, in consequence, a comparatively easy task. Originally,
the couplings were intended to be flexible ones, but after a few runs of the machine
rigid couplings were found to be better and such were used. Much of the work
connected with the couplings and other fittings to the machine was carried out in the
Engineering Department of the Laboratory, and we are greatly indebted to
Dr. Stanton, the Superintendent, for much advice on these matters.

At first there was trouble with the bearings. The clearance allowed was very small,
and after the machine had run for one or two hours the expansion of the shaft was
sufficiently great to cause a collar to come into contact with one of the bearings.
Increased clearance was allowed and the difficulty disappeared. From that time
(April, 1911) no portion of the machine has given the slightest trouble. The parts
are so exactly balanced that the tremor of the concrete base is almost too small to be
detected. This is fortunate, as during the observations for an absolute measurement
of a resistance, two microscopes are mounted on the concrete bed and used to gauge
the distance apart of two coils within a thousandth of a millimetre. These measurements
were frequently made when the speed of the machine was 1040 revolutions per
minute, but an accuracy within a thousandth of a millimetre was obtained with little
trouble. During the progress of our work the machine has been admired by many
hundreds of visitors to the Laboratory, and the kindness of Sir Andrew Noble in
having the heavy metal work carried out at Elswick is greatly appreciated.

To place the cylinders in position on the cradles, the portions of the shaft supporting

the discs were removed from their bearings, the cylinders threaded over the shafts

into approximately correct positions and the shafts restored to their proper places. To

prevent damage to the cylinders during this operation, a framework of wood was built

to support the shafts and cylinders and to enable them to be lifted as one piece. The

cradles on which the cylinders are supported are provided with stops and clamping

screws to prevent any marked relative movement of a cylinder and the cradle on which

it rests.

Section 15. — Insulation Tests.

When making an absolute measurement of resistance, the greatest difference of
potential between any portion of the circuit and the earth was about 130 volts, and
the greatest difference of potential between neighbouring turns of wire on any one

The insulation resistance between the circuit and the earth was tested each day on
which measurements of resistance were made. For the insulation test, the earth wire

VOL. CCXIV. A. K

66 MB. F. E. SMITH ON THE ABSOLUTE MEAStJEEMENTS OF A

(p. 85, fig. 19) was removed, and the voltage applied to the circuit was the same
as that used for the resistance measurements. The insulation resistance was always
greater than 1000 megohms.

To measure the insulation resistance between the coils, the latter were usually arranged
in two groups, each group consisting of one coil from each cylinder. At first, with an
applied voltage of 20 volts, the insulation resistance was about 10,000 ohms. The
insulation resistance of coils on cylinders Nos. 2, 3, and 4 proved to be well above
1000 megohms, but that on the coils on cylinder 1 was low. We found these coils to
be in close proximity to, or in contact with, a few crystals of pyrites, and after
dislodging these, wholly or in part, the insulation resistance increased to above 1000
megohms. No trouble has since occurred. As the coils are of bare copper wire and
are covered only with a thin wrapper of silk, we think it necessary to make an
insulation test of the coils on each day that resistance measurements are made. The
test occupies but a few minutes, and during our work it was regularly made.

The insulation resistance between the earth and the rotating wires attached to the
discs was usually tested at 20 volts. The results in all cases were satisfactory. For
certain measurements, it is essential that the rotating wires be insulated from each
other and as the wires may not occupy exactly the same positions with respect to the
disc and shaft when rotating, as when stationary, the tests are preferably made with
the machine running. The test when the wires are rotating is of some interest. One
terminal of the galvanometer is connected to one brush, and one pole of the battery to
the remaining four brushes, the five brushes being in contact with the segments on
one of the discs. The other terminal of the galvanometer is connected to the remaining
pole of the battery. From fig. 5, given on p. 42, it is clear that when the discs are
rotating one terminal of the galvanometer is always connected to one or two of the
rotating wires, and the other terminal, through the battery, is connected sometimes
with four and sometimes with eight of the wires. The wires are continually changing
in position and the deflection of the galvanometer enables the insulation resistance to
be calculated. The first set of conducting wires which were used became faulty in
insulation resistance because of the action of some insulating tape which was used to
bind the wires together. They were replaced by others which were supplied with
double layers of silk and which we subsequently shellacked and encased in silk tubes.
No trouble has since been experienced, the insulation resistance being well over 200
megohms. The insulation of the remaining part of the circuit, e.g., leads to brushes,
standard resistance, &c, was frequently tested, but no fault was found.

Section 1 6 .— Me asurement of the Diametral Distance between

Opposite Segments.

The distance between opposite segments was measured both when the discs were
stationary and when running at speeds varying from 170 to 1110 revolutions per
minute.

RESISTANCE BY A METHOD BASED ON THAT OF LOEENZ.

67

For the stationary measurements, two micrometer heads were fixed to, but
insulated from, two short upright rods of brass secured to a stout bar of the same
metal, the distance between the contact faces of the micrometer screws being
approximately equal to the distance between opposite segments. This gauge was
supported on two uprights secured to the slide rails of the Lorenz apparatus and
adjusted in position for the measurement of a diameter. Between the segments and
the micrometer screws, vertical wires of phosphor bronze, similar to those used for the
brushes, were interposed, and the measured distance was taken as equal to the
distance apart of the segments plus twice the diameter of a wire. Contact between
a segment and a micrometer head was indicated by the buzzing of a telephone due to
the passage of a small alternating current through a circuit including the telephone,
the micrometer head, and the segments. Four measurements were made on each pair
of segments lying on opposite sides of a diameter and the mean of the 20 measure-
ments was taken as correct. Such a series of measurements was frequently taken
and show the wear of the segments, due to their friction with the brushes, to be
comparatively slight. As examples, we give the results of some measurements made
in December, 1912, and in June, 1913.

Table VIII. — Giving the Diametral Distance between Opposite Segments.

Segments.

Disc No. 1.

Disc No. 2.

December, 1912.

June, 1913.

December, 1912.

June, 1913.

1 and 6

2 „ 7

3 „ 8

4 „ 9

5 „ 10

cm.
53-581
•579
•579
•579
•584

cm.
53-562
•566
•569
•573
•570

cm.
53-556
•556
•550
•556
•554

cm.
53-546
•547
•546
•549
•560

of segments . . J

53-580

v .

53-568

53-554

i

53-550

53-574 cm.
= 26-787 cm.

Y

53-552 cm.
-26*776 cm.

The standard of length used was an invar rod with approximately flat ends, and
measurements on this rod were made in the same way as those on the segments.

When the discs were rotating, contact with the segments was made by advancing
a brush by means of a micrometer screw until a telephone indicated the completion of
a circuit as in the previous measurements. The micrometer head made contact with
the brush holder through the medium of a small steel hemisphere attached to the

K 2

68

MR F. E. SMITH ON THE ABSOLUTE MEASUEEMENTS OF A

holder, and good contact was ensured by a spring attached to the supporting ring and
brush, which forced the latter towards the micrometer screw. The brush wires were
put under considerable tension and petrol was used as a lubricant. Measurements
were made at speeds varying from 170 revolutions per minute to 1110 revolutions per
minute, the speed being registered by the directly driven chronograph. The results
of three sets of measurements are plotted in fig. 14. The relation between the

MM.

0*05

if) '04

D

Q

o

■

«

<

/ '/

03

Z

r*

r t

£ 02
<

%

1____4

5

Z 'Ol

o

ifc/6

■"o

o

a

N 1 K

IO

«Z

10"

N= N°

>F REVOLUTIONS

Fig. 14.

14-

PER MIN

increase in radius and the square of the number of revolutions per minute is
dr = 3'7n 2 x 10~ 8 , where dr is the increase in radius in millimetres and n is the
number of revolutions per minute. The normal speed of the apparatus when resist-
ance measurements are in progress is about 1050 per minute, and the mean radius is
then 0*04 mm. greater than the mean value given in Table VIII. The effective
radial distance at 20°'0 C. of the segments is therefore 26787 + 0*004 = 26791 cm.
for disc No. 1 and 26776 + 0'004 = 26780 cm. for disc No. 2.

Section 17. — Determination of the Distance between the Centres

of the Coils.

The distance between two coils on opposite sides of a disc has to be known with
considerable precision, as a change of three-thousandths of a millimetre in this distance
changes the mutual inductance of the coils and discs by 1 part in 100,000. As it is
not possible to make direct measurements of this distance with both rapidity and
precision, we followed the plan adopted by Glazebrook # (and by Lord Rayleigh in
1882) of reversing the coils, without interchange, and then repeating the resistance

* i

Phil. Trans.,' vol. 174, p. 251, 1883.

RESISTANCE BY A METHOD BASED ON THAT OF LORENZ.

69

measurements. Reference marks are made on the flanges of the cylinders , and when
the coils are parallel the mean distance between two such marks, one on each cylinder,
in the two positions of the coils, is. exactly equal to the mean distance between the
mean planes of the coils. If there are two marks diametrally opposite on each cylinder
and two distances are measured for each position of the coils, the mean distance between
the marks is the mean distance between the centres of the coils if the latter are
approximately parallel. In our case a want of parallelism of 0*25 degree (far in excess of
that met with in practice) introduces an error of less than 1/x, in the determination of
the distance between the centres of the coils. In practice we have four marks on
each cylinder, these being at approximately equal distances from the mean plane of
a coil, and the distance of each mark from such plane is known within 10/x, or 20/x.
The vertical distances of the marks from the axis
of the coil are the same within O'l mm., and for
the measurements under consideration the dis-
tances may be regarded as identical.

Fig. 15 represents diagrammatically two cylin-
ders at a mean distance 00 ; apart. When the
coils are parallel, the distances ac, eg, bd, and fh
are approximately equal to 00 ; . When the coils
are reversed but not interchanged, the distances
are in general different from what they were before ;
let the distances be aV, e f g\ &c. With parallel
coils each of the mean distances (ac + aV)/2, (eg + e'g')/2, &c, is equal to the average
distance apart of the mean planes of the coils. If the two coils are not parallel but
very nearly so, the average of the distances ac, a!c\ eg and e f g r is equal to the average
of the remaining four distances and also equal to the average distance apart of the
centres of the coils.

In the flanges of each cylinder four brass plugs are screwed and cemented in
position. The plugs in each flange are at opposite ends of a diameter, and the four
plugs in one cylinder are contained in a common axial plane. Fig. 4 shows two of the
plugs ab in cylinder No. 3, and two cd in cylinder No. 4. On the faces of the plugs
thin rectangular pieces of platinum are soldered ; the surfaces of these are polished,
and a scale of half millimetres, cut at right angles by two horizontal lines, half a
millimetre apart, is engraved on each piece. The scales were engraved by the late
Mr. Donaldson of the Metrology Department.

For the measurement of the distances, two microscopes are mounted on a special
platform supported on a tripod, the base of which can be clamped to the bed of the
Lorenz machine by means of the wing nuts w 9 w\ w'\ &c, shown in fig. 4, and by
means of screws the platform can be given the necessary movements to enable both
microscopes to be rapidly focussed without any change in their relative position.
When the platform is clamped by the wing nuts 'ww\ the lines on the plugs a and c

70

ME. F. E. SMITH ON THE ABSOLUTE MEASUREMENTS OF A

are under observation, and when, the platform is clamped by means of w f and w", the
lines on plugs b and d can be viewed, and so on for the remaining positions.

The reference standard is a scale of half millimetres, engraved on invar. The scale
was standardised by Mr. Attwell before making any absolute measurements of
resistance, and again after their completion. The results on the divisions employed
in our work agree within less than 1/x.

The general procedure in making the measurements was to observe the invar scale,
then the eight plug distances, and finally the invar scale again. The first and last of
the observations agreed in general within 1/m or 2/x. An absolute measurement of
resistance immediately followed and then another set of observations was made on
the invar scale and the plugs. The coils were not reversed in position until a large

The distance between coils Nos. 1 and 4 and between Nos. 2 and 3 is required with a
much less degree of accuracy, an error of 1 mm. in both of these distances producing a
change in the mutual inductance of less than 1*5 parts in 100,000. As the distances
between coils Nos. 1 and 2 and Nos. 3 and 4 are known from the previous measurements
within a few thousandths of a millimetre, it was only necessary to measure the
distance 1 to 4, or 2 to 3. In practice we measured the distance between a plug on
cylinder 2 and a plug on cylinder 3, and employed for this purpose a brass bar with
half-millimetre divisions engraved at the ends ; this enabled the distance to be
determined within about 0M mm. The distances of the plugs from the mean diametral
planes of the coils were known and no further measurements were therefore necessary.
Instead of measuring the distance between two coils such as Nos. 2 and 3, we may, as
an alternative, measure the distance between the two sets of five brushes, and a number
of such measurements were made as checks.

Section 18.— Calculation of Mutual Inductance of the Coils and the

Contact Circles of Segments and Brushes.

The arrangement of the coils and discs in the instrument may be represented
diagrammatically in section by fig. 16. The coils are numbered 1, 2, 3, and 4, and the
discs are denoted by D 1 and D 2 .

K

A

B

C E

H

D.

D

Fig. 16.

The mutual inductance M of any one coil and the contact circles is calculated in two
parts. The first part gives the mutual inductance M x of the coil and the circumference

KESISTANCE BY A METHOD BASED ON THAT OF LORENZ. fl

of the disc nearer to it, and the second part gives the mutual inductance M 2 of the
coil and the circumference of the other disc. The difference of these is required, so
that M = Mi-Ma.

To find M 1? two mutual inductances were calculated, viz., that between D x and a
coil of length BC, and that between D 1 and a coil of length AC. The difference of
these mutual inductances gives M x . If the coils on the four cylinders are exactly-
similar the values of M x are identical.

To find M 2 for coils Nos. 1 and 4, the mutual inductances were calculated between
D 2 and a coil of length BK and that between D 2 and a coil of length AK. The
difference is equal to M 2 . To find M 2 for coils Nos. 2 and 3, the mutual inductances
required are that between D 2 and a coil of length EK and that between D 2 and a coil
of length FK.

In the Lorenz apparatus, the distances of the coils from the discs can be varied.
This changes the mutual inductance and the rate of change of M with variation of
axial distance must therefore be known.

To find M x we used the following formula due to J. Vireamu Jones #

M = Q(A + a)ck l^~ + ^(F-II)

In this expression, is the angular length of the helix, A the radius of the helix,
a the radius of disc or contact circle, and x the axial length of helix.

c 2 = 4Aa/(A + a) 2 , c' 2 =l-c 2 ,
W = 4 Aa/( A + of + x\ ¥ 2 = 1 - k\

F, E, and II, are complete elliptic integrals of the first, second, and third kinds
respectively ; F and E are to modulus Jc, and

n = p ^

Jo (l—c 2 sr

(l-^sin^Hl-Fsin 2 ^) 1 '

Putting c f jM = sin /3, the quantity (F— II) can be expressed in terms of complete
and incomplete integrals of the first and second kindsf ; thus

c- 1 ^ 2 sin £ cos P (F-II) = - ^tt-F (*) F (&', \$) +E (jfe) F (k\ 0) +F (*) E (&', /J).

The various elliptic integrals required were calculated by interpolation from
Legendre's tables, but as a check on possible misprints in the tables a number of the
integrals were calculated directly by successive quadric transformation.!

The dimensions chosen for calculating the values of M x are given in Table IX. The

* J. V. Jones, 'Koy. Soc. Proc./ vol. 63, p. 198, 1898.
t Cayley, * Elliptic Functions/ § 183.
t Cayley, Chapter XIII.

72

MR. F. E. SMITH ON THE ABSOLUTE MEASUREMENTS OF A

dimensions of the coils and discs differ from these values by small amounts dA for
the radius of the coils, da for the radius of the discs, and dx for the length of the
coils. Small corrections to the calculated values in Table IX. have therefore to be
applied. These corrections are obtained by application of the increment formula

dM dA , da , dx
M * A* a ■ x

which gives the change in M due to small changes in dimensions, A being the radius
of the coil, a that of the disc, and x the axial length of the coil ; g, r, and s are
coefficients which are given by the expressions

Qck

g=_A|F+^(F-II)J

M

\jCfv TQ1 XjL a /T71 TT\

M 2A

«l.®^(A + a )jfl-^F-?,E

M

¥

¥

The sum q + r + s is always equal to unity.

In Table IX. we give in columns 1, 2, and 3 the constants employed for the
calculation of nine mutual inductances ; in column 4 the values of the mutual
inductances ; and in columns 5, 6, and 7 the values of g, r, and s, which are required
in our work. Table X. gives the difference values M x .

Table IX.— Calculation of Mutual Inductance.

A = radius of coil, a = radius of circle (disc), x = length of coil.

The number of turns per centimetre length of the coil is 12.

A.

a.

*v.

M.

1

f.

5.

cm,

cm.

cm.

cm.

-■■■.

17-

9419

26'

7870

23-2650

52702'

37

2*1003

-0-5737

-0-5265

17-

9419

26'

7870

7'

2635

23682-

39

2-4007

-1-2626

-0-1381

17'

9419

26'

7870

23'

3150

52755

•93

2-0998

-0-5724

-0-5274

17'

9419

26

•7870

7'

3135

23822

•74

2-3991

-1-2596

-0-1396

17

•9419

26

•7870

23'

2900

52729

•18

2-1000

-0*5731

-0-5270

17

•9419

26

•7870

7'

2885

23752

•65

2-3999

-1-2611

-0-1388.

17

•9419

26

•7870

19

•285U

47883

•64

2-1404

17

•9419

26

•7870

11

•1678 8

33534

•20

2*2880

17-9419

26-7870

15-2572 5

41656-11

2-2001

i

In Table X. the first difference values are the mutual inductances of a coil
16*0015 cm. long and a circle of radius 26*7870 cm., when the mean diametral plane

EESISTANCE BY A METHOD BASED ON THAT OF LOEENZ.

73

of the coil is distant from the circle 15'2642 5 cm., 15'2892 5 cm., and 15*3142 5 cm.
respectively. In these three positions an increase in the radius of the coil of 10 jut,
increases the mutual inductance by 3'001, 2*995, and 2*988 respectively, and an
increase in the radius of the circle of 100 /x increases the mutual inductance by —0*125,
— 0*099, and —0*072 respectively. If we have two such coils, one on each side of the
circle, the intensity of the magnetic field at the circumference of the circle will be
zero when the mean planes of the coils are about 30*656 cm. apart and the circle is

Table X. — Difference Values of Mutual Inductance.

a = radius of circle .

x = Axial length of coil .

M = mutual inductance
Difference value = Mi .

dM. for elk = 10/x
Difference value .

dM. for d A - 100/x .
Difference value . .

17-9419

26-7870

23-2650

52702-37

17-9419

26-7870

7-2635

23682-39

29019-98

+ 6-169

+ 3-168

+ 3-001

11-288

11-163

Y~

0-125

17-9419

26-7870

23-2900

52729-18

v.

17-9419

26-7870

7-2885

23752-65

28976-53

+ 6-172

+ 3-177

— y-

_J

+ 2-995

-11-281

— V"

-11-182

>

-0-099

17-9419

26-7870

23-3150

52755-93

17-9419

26-7870

7-3135

23822-74

28933-19

+ 6-174

+ 3-186

^r

+ 2-988

-11-274

-11-202

0-072

midway between them. The same result is of course brought about by a slight
reduction in the diameter of the brush contact circle, an inevitable result of wear and
re-turning of the surface of the segments. However, exact realisation of this condition
is unimportant since for the positions of the coils dealt with in the calculations, the
maximum change in the mutual inductance is only 4 parts in 1,000,000 for a change
in the diameter of the circle of one-fifth of a millimetre. Exact centering of the
circle between the coils is also unimportant as will now be shown.

When the distance of the circle from each of the mean diametral planes of the coils
is exactly 15*2892 5 cm. the total mutual inductance of the two coils and the circle is
57953'0 7 . If the circle is moved so as to be 0*25 mm. nearer one of the coils the
total mutual inductance is increased to 57953*1 7 , i.e., about 1 part in 600,000 greater
than before. Hence with a brush half a millimetre wide the variation of potential
from wire to wire will not exceed 1 part in 600,000. In practice the brushes
commonly used consisted of three parallel wires, the extreme width being about
0*5 mm.

vol. ccxiv. — A.

L

74

ME. F. E. SMITH ON THE ABSOLUTE MEASUREMENTS OF A

Table XL gives the constants used and the results obtained in one of the calculations
dealt with in Table X. and gives also the dimensions of the Lorenz coils and brush
contact circles at 20°"0 C. Table XII. gives (l) the differences of dimensions of the
coils and standard, and (2) the mutual inductance M x of each coil and the contact
circle nearer to it.

Standard.

Coils on cylinder No. —

1.

2.

3.

■ 4.

A = radius of coil in centimetres .

x = length of coil in centimetres .

a = radius of circle in centimetres

d = distance of mean diametral!
plane of coil from the circle >
in centimetres .... J

n = number of turns .....

Mi = mutual inductance of coil")

and circle ...... J

17-9419
16-0015

26*7870

15-2892 5

16*0015x12
28976*54

17-9403 r

16-0018

26*791

192

17*9408

16-0014

26-791

192

17-9427

16*0054

26*780

192

17*9433
16*0054

26*780

192

We summarise below our knowledge of the changes of M x with changes in the
dimensions of the coils and disc when the distance of the mean diametral plane of the
coil from the brush contact circle is equal to 15*2892 5 cm.

1. Increase in radius of a coil by 10/x . . . . . .

2. Increase in radius of contact circle by 10/x . . .

3. Increase in length of coil by 10/*, the position of the

mean diametral plane remaining constant, and the
number of turns increased so that there may still
be 12 turns per centimetre . . .

Change in M x .
+ 2*995

-0*0099

~\

5,

+ 1-940

J

4. Correcting factor to reduce the mutual inductance \ 16/length of coil in
to a coil of exactly 192 turns is ...... J centimetres.

The values of M l given in Table XII. hold good only when the mean diametral plane
of the coil is 15*2892 5 cm. from the circle. For other slightly different distances
we may readily calculate the corrections from the data given in Tables IX. and X.
The mutual inductance of the coils on cylinders Nos. 1 and 2 and the brush contact
circle No. 1 is 579397 when the distance between the mean planes of the coils is
30*5785 cm., and the corresponding values for the coils on cylinders Nos. 3 and 4 is

KESISTANCE BY A METHOD BASED ON THAT OF LORENZ.

75

57955*4, the temperature being 20°*0 C. For an increase in the distance apart of the
mean planes of Nos. 1 and 2 by 250^ the mutual inductance diminishes by 43*43, and
for a decrease in the distance by the same amount the mutual inductance increases
by 43*32. The corresponding values for cylinders Nos. 3 and 4 are practically
identical, being 43*48 and 43*37 respectively.

Table XII. — Giving the Mutual Inductance M a of the Coils and Contact Circles on
the Assumption that the Hadius is at all Points Equal to the Mean Radius and
that the Pitch is Uniform.

Coils on cylinder No. —

1.

2.

3.

4.

Differences.

Correc-
tion
to Mi.

Differences.

Correc-
tion
to Mi.

Differences.

Correc-
tion
to Mi.

Differences.

Correc-
tion
to Mi.

fjb.
dk. =--15-3

dx = + 3
da = +40

For number V
of turns n J

Total 1
correction J

-4-58

+ 0-58

. -0-04

-3'26
-7-30

dk = -11
dx = - 1
da = +40

-3-29
-0-19
-0-04

-2-54
-6-06

dk = + 8
dx = +39
da = - 70

+ 2-40
+ 7-57
+ 0-07

-9-78
+ 0-26

ft.

dk = +14
dx = +39
da = - 70

+ 4-19

+ 7-57
+ 0*07

-9*78
+ 2-05

Mi = 28969-24

Mi = 28970-48

Mi = 28976-80

V . ,,. ,. . ,-,.

Mi = 28978-59

Sum -57939*7

Sum - 57955-4

With change of temperature the mutual inductance varies owing to the expansion
of the coils and discs. If the distance apart of the mean diametral planes of the coils
is kept constant, the temperature coefficient of M 1 is readily calculated to be 1*06 x 10~ 5
for an increase in temperature of 1° C.

We have previously stated that it is not necessary to know the axial length of a
coil with great accuracy. From the data given on page 74, it is clear that if the
coils increase in length by 10/*, the change in M x for the coils on any one cylinder is
+1*94. But this supposes the number of turns to increase in the ratio 16*0010/16*0000.
Since the number of turns is constant the real change is 1*94 + 28970— 28970 x
(16*0010/16*0000) = 0*13. That is, a change of 10 M in the axial length of the coils
produces a change in the mutual inductance of the coils and discs of about 5 parts in
1,000,000.

L 2

76 ME, F. E. SMITH ON THE ABSOLUTE MEASUREMENTS OF A

Calculation of M 2 , the Mutual Inductance of the Coils > and the farther Brush

Contact Circle.

The following formula, due to Rosa and Grover,^ gives the mutual inductance
of a single layer coil of length x and a co-axial circle of radius A in the plane of one
end of the coil : —

M = 2A 2 N

3a 2 A 2 5a 4 AV 35q 6 A 6 y 63a 8 A 8
8 d" 64 d 8 2 512 d 12 4 1024 cP

d
where

X 2 - 3-4^/A 2 ,

X 4 = 5/2-1 (te 2 /A 2 + 4^ 4 /A 4 ,

X 6 = 35/l6-~35^ 2 /2A 2 +21^ 4 /A 4 -4^7A 6 ?

N = total number of turns in length x,

x = axial length of coil,

d = vV + A 2 .

When the coil is long this formula is very exact and easy to use, and it was a
simple matter to calculate M 2 with the precision necessary for our work. The results
of 16 calculations are given in Table XIII.

In Table XIV. the values of M 2 are given for coils, the mean diametral planes
of which are distant from the brush contact circle by the amounts given in column 4.
The results show the variation of M 2 with change (l) in the axial distance of the
coils, (2) in the radius of the coils, and (3) in the radius of the contact circle of
segments and discs.

The summary on p. 78, Table No. XV,, relates to the coils and brush contact
circles of the Lorenz apparatus and sufficiently indicates how small corrections were
made when the distance between the coils was varied. The contact circle of segments
and brushes was practically in the midplane of the coils near to it ; the method of
ensuring this is described in Section 22.

Correction for Conicality of Coils.

The increment coefficient q (Table IX.) enables the change of mutual inductance to
be calculated when the radius of a coil is changed by a small amount, but the change
must be a uniform one. When the change is not uniform, the change in mutual
inductance for an increase in radius of any part of a coil must be known, and the
correction for conicality must be calculated in parts. In the past it has been
customary to take the radius of a coil as absolutely uniform from end to end, but
such a procedure invariably introduces errors into the calculation.

* i

Bur. of Standards Bull.,' vol. 8, No. 1, p. 101.

RESISTANCE BY A METHOD BASED ON THAT OF LQRENZ.

77

Table XIII. — Calculations of Mutual Inductance.

circle.

cm.

26-7870

26-7870
26-7870
26-7870
26-7870
26-7870
26-7870
26-7870
26-7870
26-7870
26-7870
26*7870
26-7370
26-7370
26-7370
26-7370

of 12 turns

per centimetre

length.

cm.
17-9419

17-9419

17-9419

17-9419

17-9419

17-9419

17-9419

17-9419

17-9369

17-9369

17-9369

17-9369

17-9419

17-9419

17-9419

17-9419

Length of
coil.

cm.
144-1

160-1

174-6

190-6

144-4

160-4

174-9

190-9

144-1

160-1

174-6

190-6

144-1

160-1

174-6

190-6

Mutual

inductance of coil

and circle.

74981-04
75215-30
75376-21
75514-07
74986-12
75219-06
75379-13
75516-33
74939-24
75173-38
75334-19
75471-98
74985-66
75219-08
75379-42
75516-78

Mutual
inductance
differences

= M 2 .

234-26

r

137-86

232

•94^

>

137

•20

234-14

137-79

233-42

137-36

Sums of
differences.

372-12

370-14

371-93

370-78

Table XIV. — Mutual Inductances M 9 .

Length of coil of
192 turns.

Distance of mean

diametral plane of

coil from circle.

M 2 . .

cm.

cm.

cm.

cm.

26-7870

17'

9419

16'

152

1

234

•26

26-7870

17'

9419

16

152

•4

232'

94

26-7870

17'

9369

16

152

1

234

•14

26-7370

17*

9419

16

152'

1

233

'42

26-7870

17

'9419

16

182

•6

137

'86

26-7870

17

•9419

16

182

'9

137

•20

26-7870

17

•9369

16

•o

182

•6

137

•79

26-7370

17-9419

16-0

182-6

137-36

78

MR. F. E. SMITH ON THE ABSOLUTE MEASUREMENTS OF A

Table XV. — Mutual Inductances M 9 .

Distance apart of

mean planes of

coils.

cm.

Distance apart of
contact circles.

cm.

circle 2.

cm.

cm.

M*

Giving M 2 of Coils on Cylinders Nos. 1 and 2, with the Contact Circle of Disc 2.

30-20
30-50
30-50
30-50
30-55
30-60
30-80

167*50

26-

167-35

26-

167-65

26-

167-50

26-

167-50

26-

167-50

26-

167-50

26-

7800
7800
7800
7800
7800
7800
7800

17
17
17
17
17
17
17

9406
9406
9406
9406
9406
9406
9406

370
371
369
370
370
371
371

57
89
91
90
95
01
23

Giving M 2 of Coils on Cylinders Nos. 3 and 4, with the Contact Circle of Disc 1.

30
30
30
30
30
30
30
30

20
50
50
50
55
60
70
80

167
167
167
167
167
167
167
167

50
35
65
50
50
50
50
50

26
26
26
26
26
26
26
26

7910
7910
7910
7910
7910
7910
7910
7910

17
17
17
17
17
17
17
17

9430
9430
9430
9430
9430
9430
9430
9430

370
372
370
371
371
371
371
371

94
27
28
27
32
38
49
60

The change in mutual inductance for an increase in radius of any section of the
coil is most readily calculated by finding dM/dA for the brush contact circle and a
second circle of the same radius as the coil, the distance apart of the two circles
varying over the length of the coil.

Table XVI.

d = distance

apart of the

circles.

Radius of first circle = 26*787 cm.

Change in M for

change of 10/x

smaller circle.

cm.
17*9141

cm.
17*9419

cm.
17*9697

Y

-M =

' ,. . A

cm.
23*3150
19-2851
15-2573
11-1679
7*3135

88*8782
232*7922

89*1121
113-5449
145-4984
187*1127
233*5633

89*3456
113-8412
145*9000
187*6662
234*3348

0*0084
0-0107
0*0145
0*0199
0-0278

RESISTANCE BY A METHOD BASED ON THAT OF LOKENZ.

79

In Table XVI. we give the values of the mutual inductance of two such circles.
The radius of one circle is 26787 cm. and the radius of the other circle varies from
17*9141 cm. to 17*9697 cm. In column 5 of the table we give the change in M for a
change in radius of the smaller circle of 10/x.

The values in columns 1 and 5 were plotted and the resulting graph was employed,
in conjunction with the values of the diameters used in plotting the conicality curves
(fig. 12), to calculate the correction for the conicality of the coils. The method is so
obvious that we need only give the results.

Table XVII. — Corrections to M x for the Conicality of the Coils.

Coils on cylinder

No.

Correction to Mi.

Eing end of cylinder
near disc.

Eing end of cylinder
away from disc.

1

2
3
4

-0-589
-0-571
+ 0-295
+ 0-200

+ 0-942
+ 0-494
-0-326
-0-153

The mutual inductance of one coil and a disc circumference is about 30,000 cm.,
and when cylinder No. 1 is reversed in position a change of 1*5 in M b or 5 parts in
100,000, is brought about by the conicality of the coils.

Correction for Variation in Pitch.

The graph of the difference measurements of a coil absolutely uniform in pitch is a
straight line such as OP, fig. 17. Such a coil may be called a perfect coil and any
short section of it a " perfect section." That there is a difference in the mutual
inductance of a " perfect " section such as OAP and a circle, and an actual section
such as OBP and the same circle, is easily
seen. With the exception of the wires
at O and P, every wire in the actual
section is farther from the circle than the
corresponding wires in the perfect section,
and the mutual inductance of the former
section will in consequence be the smaller.

(

V

t

>y\

KC

)

A

/

2b>u.

tx_ —

►

■+*-

_ ~A

P

\ '

Fig. 17.

If the periodic curve is symmetrical with respect to the " perfect " curve, the reverse
is true for the next section, but the difference is not so great and hence there is not
perfect compensation. As we proceed along a coil with such periodic variations the

80

MR F. E. SMITH ON THE ABSOLUTE MEASUREMENTS OF A

individual corrections are alternately plus and minus, and the total effect of these
half-period elements depends on the difference of phase at the beginning and end
as in the case of diffraction effects in light.

To obtain the corrections we have calculated the mutual inductance of small
portions of the coils and the corresponding circles. The mutual inductances calculated
are (l) those of the circle and of coils each of which is 0*635 cm. in length, the
distance between the circle and the end of the coil nearer to it increasing from
7*3885 cm. to 23*2635 cm. in steps of 0*635 cm. ; (2) those of the circle and of coils,
each 25/x long, the distance between the coil and circle increasing from 8*0235 cm. to
23*2635 cm. in steps of 1*27 cm. In all cases the number of windings on a coil is at
the rate of 12 turns per cm. The results of these calculations were plotted and by
means of the curves we have corrected for the variation in pitch.

As an illustration, let us examine the second section of coil No. 3 when the ring
end of the cylinder is nearer to the disc. For clearness, this section is reproduced in
fig. 17 and is denoted by CB. The end of the section nearer to the disc is 5/x nearer
than the end of the corresponding perfect section, and the other end of the section is
20/x farther from the disc than the other end of the corresponding perfect section.
The ratio of the lengths of the two sections is therefore 6375/6350 and the ratio of
the current densities in the equivalent current sheets is 6350/6375. The M of the
perfect section and the disc is 1723*692 ; if its length is increased by 5/m at the end
nearer the disc and by 20/* at its other end, M is increased by the amounts 1*382 and
5*340. (These corrections are obtained from the curve.) The total M is now
1730*414. If next we reduce the number of turns to its original value the M becomes
1730*414 (6350/6375) = 1723*628, and since the section is now identical with the
actual section, the correction for variation of pitch and displacement of section is
1723*628-1723*692 = -0*064 or -3*7 parts in 100,000.

In this way we have calculated the corrections for all the sections of the coils both
when the ring end is nearer to the disc and when farther from it.

The values of the corrections are as follows : —

Table XVIII.

Correction to M.

Coils on cylinder

i

No.

Eing end of cylinder Eing end of cylinder
near disc. away from disc.

1

2
3
4

1

+ 0-502
4-0-987
-0-734
-1-535

-0-369

-0-874
+ 0-536
+ 0-486

EESISTANCE BY A METHOD BASED ON THAT OF LORENZ.

81

Section 19.— Effect of Electbic Motor on the Mutual Inductance

of the Coils and Discs.

Originally it was our intention to employ a water turbine to drive the Lorenz
apparatus, but there were many difficulties in the way of a satisfactory system, and
finally we decided on an electric motor. Before coming to this decision we made a
number of experiments on the effect of the presence of a large mass of soft iron on
the mutual inductance of two coils each of 200 turns of wire and 24 cm. in diameter.
The distance between the coils could be changed and the approximate mutual
inductance between them was measured by Mr. A. Campbell. The iron employed was
a mass built up of laminated sheets tightly pressed together, the dimensions of the
mass being 35x18x8 cm. When the coils were parallel and their mean planes 7 cm.
apart, the following values were obtained for the mutual inductance when the iron
was placed on the common axis of the coils and at a distance d from their mean
plane : — ■

d in centimetres.

M in microhenries.

00

4942-5

70

4942*6

60

4942-6

39

4945-2

20

4975-0

00

4942-6

The distance apart of the coils was afterwards increased to 10 cm. and eventually
to 20 cm., but in no experiment could the effect of the iron at a distance of 1 m. be
detected by the mutual inductance measurements. The stray magnetic field produced
by the motor is not a source of trouble and has no influence on our results ; the only
manner in which the motor can affect the resistance measurements is by its action, as
a mass of iron, on the mutual inductance of the coils and discs.

The field magnet of the motor is not large ; its length parallel to the shaft is about
30 cm., and its section at right angles to the shaft is about 1000 sq. cm. The
distance from the centre of the motor to the centre of the nearest of the four coils is
almost exactly 400 cm.

Dr. G. F. C. Searle, F.R.S., who has taken great interest in our work and to whom
we tender our thanks, has very kindly calculated the effect of a sphere of soft iron on
the mutual inductance of a coil and circle, both of which are some distance away. If
the radius of the sphere is 20 cm. (corresponding roughly to a mass of iron equivalent
to our motor) and the coil and circle are of the same dimensions and the same distance
from the sphere as in the Lorenz apparatus, the effect of the sphere on the mutual
inductance appears to be about 1 part in 10,000,000 which is, of course, absolutely
negligible. This value is in very good agreement with two values determined
experimentally.

vol. ccxiv. — A. M

82 MR. F. E. SMITH ON THE ABSOLUTE MEASUREMENTS OP A

The intensity of the magnetic force, at a point corresponding to the centre of the
motor, which is produced by a current of 2 amperes through the four coils of the
Lorenz apparatus, is about 0'0025 C.G.S. units. The iron of the motor becomes
magnetised and the result is an increase in the total magnetic flux through the discs.
We had to find the ratio of this increase to the flux produced by the current in the
four coils. This ratio we have found in two ways. In both of these we magnetised
the iron of the motor by winding around it a large solenoid of 16 turns of insulated
copper wire. When a current was passed through this coil the magnetising" field
inside the solenoid was approximately in the same direction as the field due to the
four coils, i.e., practically parallel to the shaft. The iron was magnetised and the two
discs of the Lorenz apparatus were caused to rotate in the resulting field. Since the
mean field in which one disc rotated was not the same as that in which the other disc
rotated, a difference of potential was produced between the edges of the two discs.
In our experiments we compared the galvanometer deflection produced by this potential
difference with that produced by a current in the four coils of the Lorenz apparatus
when the mutual inductance of the coils and discs was changed by a known amount.
The result found is that when the iron of the motor is placed in a magnetising field of
2*5 C.G.S. units, the total effective magnetic flux through the two discs is 1 part in

' O O X

10,000 of that due to the current in the four Lorenz coils. With such a small
magnetising field as 0*0025 C.G.S. units, it was impossible to measure any effect, but

the calculated effect is — ■, i.e.> 1 part in 10,000,000.

In the second experiment we wound on a framework of wood a similar coil to that
surrounding the motor. Both coils were of 20 cm. radius and had 16 complete turns.
When a current of 5 amperes was passed through the coil, the intensity of the axial
field was measured by means of a magnetometer at distances of 1, 2, 3, and 4 metres
from the mean plane of the coil. Similar measurements were made along the axis of
the coil which surrounded the motor, the current through this coil being 5 amperes as
before. The results are of interest and are given in Table XIX.

The nearer disc of the Lorenz apparatus is about 400 cm. from the centre of the
motor, and we may take the magnetic force due to the motor as uniform over this
disc. The area of one face of the disc is 2200 sq. cm. so that the total flux through
it due to the iron of the motor was 2200 (0*0010-0*0003) = 1*5. Had the
magnetising force on the iron of the motor been that due to 2 amperes through the
four coils of the Lorenz apparatus, the total flux would be reduced to
(1*54 x 0'0025)/2*5 = 0*0015. The total effective flux through the two discs will be
somewhat less than this, but the reduction is not important. When making a
resistance measurement, the total effective flux through the two discs is about 24,000,
so that the magnitude of the motor effect is 0*0015/24000 = about 6 parts in
100,000,000.

The intensity of the stray field of the motor when running at full load has already

RESISTANCE BY A METHOD BASED ON THAT OF LOEENZ.

83

Table XIX. — Giving the Intensities of the Axial Magnetic Fields produced by a
Current of 2 Amperes in Two Solenoids One of which has the Motor as a Core.

Axial distance from
centre of coil.

Intensity of magnetic field.

No iron present in coil.

Motor as core of the coil.

cm.
100
200
300
400

C.G.S. units.
0-023
0-0034
0-0009
• 0003

C.G.S. units.
0-09
0-013
0-0036
0-0010

The motor was not running during these measurements.

been stated to cause no trouble. The intensity of the component of this stray field
parallel to the shaft of the apparatus and 400 cm. from the centre of the motor, was
measured to be 0'0006 C.G.S. units.

The general conclusion is that an electric motor may safely be used for such a
purpose as ours.

Section 20.— Arrangement of Circuits.

(a) Connection to Brushes. — The brushes are connected to insulated terminals fixed
to the phosphor-bronze rings, and double silk-covered copper connecting wires pass
from these terminals to a selector switch on the observation table. A diagrammatic
representation of the connections is given in fig. 19. The selector switch consists of
two conducting arms which enable the observer to complete the circuit through any
one of the five pairs of brushes by moving the contacts from stud to stud. When it is
desired to place the ten brushes in series and thereby get an induced voltage five
times as great as with one pair of brushes, conducting straps are placed in the
positions SS SS indicated by the dotted lines and the turning head makes contact
with the studs 1/ and 5. Any one of the five pairs of brushes may still be selected
and observations may be made to test if the brush contacts are satisfactory. When
the ten brushes are placed in series the thermo-electric effects are of course added
and particular care has therefore to be taken with the brushes. When trouble is
experienced it greatly facilitates the work to select pairs of brushes and so detect the
faulty ones.

To place the brushes in two sets of five in parallel, conducting straps connect
together each set of five terminals TT, &c, on the selector switch. The position of

(b) Multiple Commutator and Plug Board (fig. 19). — This is designed after the
manner of the multiple commutator used for the Ayrton- Jones current weigher, and a
short description will therefore suffice. A commutator allows of the reversal of the

M 2

84 MR F. E. SMITH ON THE ABSOLUTE MEASUEEMENTS OF A

current in both coils on any one cylinder, and the plug board allows of the reversal of
the current in any one or more of the helices. Each helix is designated by a number
and a letter which are marked on an ebonite bridge at the top of the multiple
commutator ; the turning heads are also numbered to enable changes to be rapidly
made without likelihood of error. The lower commutator reverses the current in all
of the coils.

By suitable conducting straps the coils on one cylinder may be placed in parallel
with those on another cylinder. In many of our observations the coils on cylinders
1 and 2 were placed in parallel with the coils on cylinders 3 and 4.

(c) The Reversing Switch. — Preliminary experiments indicated that the make and
break of the current through the coils had a considerable inductive action on the
galvanometer circuit. The deflection of the galvanometer thus produced amounted
at times to 50 cm., on a scale at a distance of 2 m., and prohibited such rapid
reversal of the current as we desired to make. Similar inductive action is remarked
on by Prof. J. V. Jones in the 'Report of the British Association for 1890/
Had the galvanometer circuit been a stationary one, we might have introduced a
compensating system, but this was not possible with the system of rotating conductors
we had installed. It was evident that the galvanometer circuit should be broken
before making or breaking the current circuit, and as the position of rest of the
galvanometer coil on open circuit is, in general, different from that when the circuit is
closed, it appeared desirable to have the galvanometer excessively damped when not
included in the main circuit. The switch shown in fig. 19 enables this to be done.
All the connections are shown in the figure and it is not necessary to describe the
switch in detail. On moving from stud 1 to stud 2 the galvanometer circuit is
shunted by a negligible resistance and the main galvanometer circuit is broken. On
moving to stud 3 the current is broken— on to stud 4 the current is made again but
in the reverse direction—and when the movement is continued to stud 5 the
galvanometer is again placed in the brush circuit. This switch proved very
convenient in practice and greatly facilitated our work.

(d) In addition to the commutators already described, a simple commutator was
added to reverse the potential leads attached to the standard resistance. Such
reversals were made to eliminate electrostatic effects.

(e) Galvanometer. — This was of the Ayrton-Mather type and was very kindly lent
to us for the work by The Cambridge Scientific Instrument Company, Limited. The
resistance of the galvanometer is 16 '5 ohms and the period of the coil is 5*2 seconds.
At a distance of 2000 scale divisions the sensitiveness is 57 divisions per microvolt.
The external resistance for aperiodic working is 50 ohms.

When the current through the eight coils of the Lorenz apparatus is 2 amperes
and a direct measurement of a resistance of 0*01 ohm is in progress, the difference of
potential on the standard resistance is 0'02 volts. In making the measurements the
current is reversed, and on reversal there is a change in the rest point of the

RESISTANCE BY A METHOD BASED ON THAT OF LORENZ.

85

C

R

AAAAAt

<S>

B

~-J

Fig. 18. Simple diagram of circuit.
R, resistance to be measured ; B, battery ; Gr, galvanometer.

TO BRUSHES

ON DISC I

TO BRUSHES

ON Dl SC 2

i i i i i

12 3 4-5
9 6 O^O.OT

fO

(f)

or
Q

z

-J

>

o

z

o

if) <\l

5
o

dddiS

O

Fig. 19. Detailed diagram of circuit.
A, ammeter ; B, battery ; C, brush selector switch ; D, resistance in galvanometer circuit ; E, earthed
point on circuit; G, galvanometer; M, multiple commutator and plug board; E, resistance to be
measured ; S, reversing switch.

86

MR. F. E. SMITH ON THE ABSOLUTE MEASUREMENTS OP A

galvanometer spot of 57 mm. (at 2 m.) per microvolt. To obtain a precision of 1 part
in 100,000 on a single reading it is necessary, therefore, to note the change of
deflection when the current is reversed with an error not greater than 11*4 mm.
When the motion of the coil is made aperiodic by introducing additional external
resistance, the sensitiveness is about one-quarter of the previous value, and the error
of the difference reading must not be greater than about 3 mm. For measurements
of a resistance of 0*001 ohm the difference of potential on the standard resistance was
about 0*004 volt and the change of deflection had to be read with an error not greater
than 0*6 mm. For a single measurement of a resistance about fifty different readings
were taken and the mean of these is used to calculate the result (see p. 98).

Fig. 18 is a simple diagram of the circuit and requires no explanation. Fig. 19 is
a more detailed diagram and shows the connection of the circuit to earth.

Section 21.— Standard Kesistances.

The resistances measured in absolute measure were of nominal values 0*001 ohm,
0*002 ohm, and 0*01 ohm. The first and last of these were standard manganin
resistances capable of carrying currents of 30 and 10 amperes respectively without

increasing in temperature by an appreciable amount.
The currents used in our measurements did not exceed
4 and 2 amperes ' respectively, and the heating effect
due to these currents could not be detected.

To obtain an effect corresponding to that of a resist-
ance of 0*002 ohm, three standard resistances were
arranged in a triangular fashion (fig. 20) as first
suggested by Lord Bayleigh. # The resistances
are of the well-known type introduced by the
Physikalisch-Technische Reichsanstalt ; they are of
manganin and the mean temperature coefficient in the
neighbourhood of 20° C. is about + 15 parts in 1,000,000
per degree rise of temperature. The resistance (a) fig. 20 is a coil of 2 ohms
resistance, (6) is a 1-ohm standard, and (c) consists of a coil of 1000 ohms shunted by
others having values from 100,000 to 500,000 ohms. If the current in the main

circuit is i the current through b is =— — =- where L is the summed value of the

a + b + c + L

resistances of the current leads to the three coils. The difference of potential at the

9 The quantity =— — =- thus takes the place of R

a+b+c+L a + b + c + L

in the formula R = M.n (p. 35) and is called the effective resistance. f The two ohm

* 'Phil. Trans./ 1883.

t A complete treatment on the combinations of a four-terminal resistance with other resistances is
given by G-. F. C. Searle, £ The Electrician/ March 31 to April 21, 1911.

extremities of b is

EESISTANGE BY A METHOD BASED ON THAT OF LORENZ. 87

coil is of special construction ; it is divided into two equal coils each of which can be
compared with the standard coils.

The coils were supported from mercury cups in a bath of well stirred paraffin oil
maintained at a constant temperature of 20°'0 0. The stirring was produced by
blowing dry air through the oil. A spiral toluene thermostat was used to control the
temperature and the heating of the oil was produced by an electric current flowing
through a resistance coil supported on a large frame at the bottom of the bath.
These arrangements are those in common use in the Electrical Standards Department,
and the results obtained are exceedingly satisfactory.

The methods adopted for the accurate comparison of the coils with other wire
standards and with mercury standards of resistance are published elsewhere, # and it
is not necessary to describe them here. All the resistances were frequently compared
with standard manganin coils which are hermetically sealed and the secular changes
in which are exceedingly small.

♦The new mercury standards of resistance of the National Physical Laboratory are
nine in number. They have spherical end vessels 4 cm. in diameter and were made in
accordance with the specificationf of the London Conference on Electrical Units and
Standards 1908. The resolution relating to the international ohm is as follows : —

" The international ohm is the resistance offered to an unvarying electric current
by a column of mercury at the temperature of melting ice, 14*4521 gr. in mass, of a
constant cross- sectional area and of a length of 106*300 cm."

Mercury standards of resistance have also been made at the Physikalisch-Technische
Reichsanstalt and the Bureau of Standards at Washington. Recent comparisons
show that the units of resistance so derived agree with the unit derived at the
National Physical Laboratory within about 2 parts in 100,000. The exact figures
are not yet to hand.

Section 22. — Setting of the Coils to be Coaxial with the Shaft and at
approximately equal distances from the brush contact circles.

(l) Setting of the Axes of the Coils to he Parallel to the Axis of the Shaft.

Mechanical Method. — -At the time of turning the marble cylinders, a phosphor-
bronze ring was let into one end of each, and the surface turned at right angles to
the axis. When the cylinders were in position on the cradles of the Lorenz
apparatus, a radial arm supporting a micrometer head was clamped in a suitable
position on the shaft and contact between the micrometer screw and each of the rings
in turn was made at three points 120 degrees apart. The making of a contact was

* 'B.A. Elect. Stands. Committee Report/ 1906.
t 'B.A. Elect Stands. Committee Eeport/ 1909.

88 MR. F. E. SMITH ON THE ABSOLUTE MEASUREMENTS OF A

indicated by a telephone, and readings could be repeated within about jO'Ol mm.
Each cylinder was adjusted in position until the three readings were identical and the
axes of the cylinders were then approximately parallel to the axis of the shaft. The
method was sensitive, but irregularities in the thrust-bearing surface of the shaft
must introduce errors which are difficult to eliminate.

(2) Setting of the Coils to be Coaxial with the Shaft.

(a) Mechanical Method. — A direct-reading spring indicator was used to measure
the perpendicular distance of the inner surface of each marble cylinder from the
surface of the shaft, and each cylinder was adjusted in position until the readings at
all points were practically identical. The indicator was sensitive to a difference of
about 0'02 mm. and the adjustment of a cylinder occupied only a few minutes. If
the inner surface of a cylinder is not coaxial with the coil, then of course an error is
introduced.

(b) Electrical Method. — -The calculations we have made give only the mutual
inductance of the coils and the brush contact circles, and it is not possible for us to
give other than general diagrams indicating the manner in which the intensity of the
magnetic field varies along the radius of a circle and other diagrams indicating the
difference of potential between the axis and any point on a radius which is produced
by the rotation of that radius. Such diagrams will, however, serve to explain the
electrical method of setting the coils.

In fig. 21 (a), DC represents the plane of rotation of one of the discs, and BB' the
position of the brush contacts. The intensity of the magnetic field produced by a current
in the coils on both sides of the disc is practically zero at BB' and changes in sign as
we pass radially outwards from the disc. The form of the intensity curve is roughly
shown by the curve EFGH. When the disc rotates, the difference of potential
between the centre O and any point A on a radius increases with increase of the
distance A to a maximum value at B and B', but afterwards it decreases. The

potential difference is given by 2irn ~Bydy where OA = y and B is the magnetic flux

Jo

at a distance y from O. The potential difference can be represented as an area if the
flux be multiplied by y before it is plotted. The area enclosed by the line DD' and
the curve KCLM shows roughly how the potential difference varies ; thus the
difference of potential between and A is represented by the area OCA. Areas to
the left of DD' are counted as positive and those to the right are counted as negative.
In our apparatus the brush and segment at B are insulated from those at B' and it is
therefore possible to measure the difference of potential between the segments and so
determine whether the field produced by the current in the coil is symmetrical with
respect to the axis of the shaft. Without the insulation of the segments, i.e., by the
use of a disc alone as in the old forms of apparatus, eddy currents in the disc produce
disturbing effects.

RESISTANCE BY A METHOD BASED ON THAT OP LORENZ.

89

The effect of displacing the coils parallel to the shaft is diagrammatically shown in
fig. 21 (6). The area OB'CS is greater than the area OLR — RNB and the difference
of potential between O and B' is greater than that between O and B. The relation
between the mean of these voltages and that obtained when the coils and shaft are
coaxial will be seen presently.

A similar change in the difference of potential between B and B ; is produced by a
rotation of a coil about a vertical axis passing through its centre. Fig. 21 (c) shows

D

(')

Fig. 21.

generally the effect produced and makes it clear that the mean diametral plane of the
coil may be set parallel to the brush contact circle by observations of the differences
of potential at such points as BB'.

The first coils to be set coaxial with the shaft by these electrical methods were
those on cylinders Nos. 1 and 4. Afterwards the mutual inductance of the No. 1
coils and the brush contact circles was made equal to that of the No. 4 coils and the
same circles by passing a current in the same direction through both and altering the
distance between the No. 1 coils and the disc nearer to them until on reversal of the
current in the coils there was no change in the difference of potential between the two
contact circles. The object of this procedure was to enable us to measure directly
the amount by which a potential difference such as OB'CS, fig. 21 (&), exceeded
the normal potential difference such as OB'C, fig. 21 (a). The circuit formed will be

VOL. CCXIV.— A. N"

90

MR. F. E. SMITH ON THE ABSOLUTE MEASUREMENTS OF A

clear from the small diagram at the top of fig. 22. One brush made contact with
one (or two) segments on each disc and the circuit was completed through the rotating
conducting wires. The displacements were read to 0*001 mm. and the changes in

-^300

-f-200 —

<

uJ + iOO
>

u ^

<
V

oo

200

300

-400

A

B

/

IO

e

6 4 2 O

DISPLACEMENT IN

2 4 6

MILL! MET RES

8

Fig. 22.

4- i5

•4- IO

+ 5

O

o

CD

id
>

o:

UJ

<

U
if)

ZQ

IO

A, change (parts in 100,000) in voltage induced by rotation of radius E due to displacement of
cylinder in direction perpendicular to its axis; B, change in mean voltage induced when five
brushes are used, touching points 72 degrees apart on edge of disc.

potential were calculated from the changes in the galvanometer deflection which were
produced on reversal of the current in the coils.

A displacement of 10 mm. increases the difference of potential between O and B' ?

RESISTANCE BY A METHOD BASED ON THAT OF LOEENZ.

91

fig. 21 (a) and (6), by about 843 parts in 100,000, and diminishes that between* O and
B, fig. 21 (a) and (6) by about 37 1 parts in 100,000. If one brush only were employed
on the segments during measurements of a resistance it would therefore be necessary
to ensure coincidence of axes of coils and shaft within about j-^u °f a millimetre, in
order that the error associated with the setting should not exceed 1 part in 100,000.

UJ

>

o

UJ

j
<

+ 200

■

B **

■

— — -M---1

■Auatfaattw

+ IOO

^\

— — — .

o

-IOO

"B

-20O

-300

\

+ 40

+ 20

O

- 20

~40

CO

UJ

>

D
U

<
U

-GO

-+

5° £° i° o f a° 3 1

4-'

5

Fig. 23.

A, change (parts in 100,000) in voltage induced by rotation of radius R due to angular displacement
of cylinder about vertical axis passing through mean diametral plane ; B, change in mean voltage
induced when five brushes are used, touching points on edge of disc 72 degrees apart,

In practice, however, five brushes are used on each disc, and when these are used in
series with the five brushes on the other disc, a displacement of 10 mm. diminishes
the voltage by (371 — 343)/2 = 14 parts only in 100,000. When the brushes on each
disc are placed in parallel the mean potential difference measured by the galvanometer

N 2

92 MR. F. E. SMITH ON THE ABSOLUTE MEASUREMENTS OF A

is nearly the mean of the separate potential differences and the error of setting is
about the same as when the brushes are placed in series. With the brushes in parallel
it is better, however, to include a resistance in series with each brush before connecting
the brushes together, for then any difference of resistance between the brush contacts
is rendered negligibly small. The observed differences of potential due to displacements
when the brushes were placed in parallel are plotted in fig. 22, and the equation of the
resulting curve is y — 0'132^ 2 where y is the change in voltage in parts in 100,000
produced by a displacement of x mm. from the coaxial position. An identical curve
results when the brushes are placed in series. It is clear that the observations enable
the coil and shaft to be set coaxial within less than 0*1 mm. and an error of this
amount introduces an error in the resistance measurements of about I part in
100,000,000.

Similar observations were made when one of the cylinders was rotated about a
vertical axis P. The results are plotted in fig. 23. The equation when the brushes
are placed in series or in parallel is y = S'5x 2 where y is the change in voltage in parts
in 100,000 produced by a rotation of x°. Thus, if x = 0*1° (a large amount) the error
introduced is 4 parts in 10,000,000.

(3) Setting of the Coils on opposite Sides of a Disc to be at the same Mean
Distance from the Contact Circle of Segments and Brushes,

The current through the coils on cylinder No. 1 was caused to circulate in the
same direction as the current through the coils on cylinder No. 4, and the resulting
flux through disc No. 1 was therefore in the same direction as that through disc No. 2.
The galvanometer circuit was completed without the inclusion of the standard
resistance R, and reversals of the current through the coils were made in the usual
manner to eliminate all effects but that due to a difference of flux through the discs,
caused by the current. In general there was a want of balance and in such case the
distance of one of the coils was changed until balance was secured or very nearly
so. With care equality could be obtained within about 2 parts in 100,000, but in
general we were content to ensure equality within about 25 parts in 100,000. This
is equivalent to equality, within about 0'07 mm. of the mean distance of the No. 1
coils from No. 1 disc, and that of the No. 4 coils from, the No. 2 disc. A similar
setting of the No. 2 and No. 3 coils was next made, and afterwards the current
through coils Nos. 1 and 3 was made to circulate in the opposite direction to that in
coils Nos. 2 and 4. If all the coils are at equal distances from the discs, there is
now no deflection of the galvanometer and the positions of coils Nos. 1 and 4 or of
Nos. 2 and 3 are changed by equal amounts until a balance is secured. The coils on
all of the cylinders are thus placed at the same mean distance, within about 0'1 mm.,
from the brush contact circles and. such equality is sufficient.

RESISTANCE BY A METHOD BASED ON THAT OF LORENZ.

93

Section 23.-— Determination of Eesistanoe in Absolute Measure.

(l) Preliminary Tests.

(A) Elimination of Error due to the Thermo-electric Effects at the Brush Con-
tacts. — -The thermo-electric effects are eliminated by observing only the change of
deflection of the galvanometer with reversal of the current in. the coils. If the
magnitude of the changes of the thermo-electric effects is considerable, and great
accuracy is desired, a large number of reversals are necessary. It becomes important,
therefore, to determine the general magnitude of the error introduced by making a
comparatively small number of reversals.

o
>

o

q:
u

O

3

9

IO

5 6 7 8

TIME IN MINUTES

Fig. 24.
A, variations in thermo-electric effects ; B, variations in thermo-electric effects plus variations in speed.

Our normal procedure in making resistance measurements was to reverse the current
in the coils at intervals of 15 seconds, and in practically all cases 48 reversals were
made. To determine to what extent this procedure eliminated the thermo-electric
effects, we operated the reversing switch with no current flowing in the coils and
noted the galvanometer deflection at the end of every 15 seconds.

The differences obtained in one such experiment are plotted against time in graph
(A) fig. 24. The mean difference from the mean is ± 0'03 mm., which would intro-
duce an error in a measurement of resistance of something less than. 1 part in

94 MR. F. E. SMITH ON THE ABSOLUTE MEASUREMENTS OF A

1,000,000. The mean difference from the mean irrespective of sign is ±0'8 mm.
These differences are typical of those obtained in our experiments and from them we
conclude that the thermo-electric effects introduce no error in our final result.

(B) Elimination of Error due to Electrostatic Effects. — -We have already described
the connections of the circuit to earth and the reversals made in order to eliminate
any electrostatic effect on the galvanometer, but we thought it desirable to make
tests from time to time of the efficiency of our arrangements. In these experiments
the coils were removed from the circuit and an equivalent resistance substituted,
which resistance was placed in such a position that the current through it produced
no magnetic field in the neighbourhood of" the discs. The standard resistance
remained in the circuit, but the leads connecting it to the galvanometer were
connected to one and not both of the potential terminals. Observations of the change
of deflection were made as before at intervals of 15 seconds. The mean difference
from the mean of such a set of measurements was always negligibly small and
indicated that no error due to electrostatic effects could influence our results.

(C) Constancy of the Speed. — -The records of speed are remarkably good and show
the variations to be very small. Each record enables the mean speed, during the
measurement of resistance associated with it, to be calculated with great accuracy ;
but a fluctuation in speed of a few parts in 100,000 lasting for a comparatively short
time cannot be detected. The metjiod adopted to control the speed is described in
Section 10, and it is evident that the speed must oscillate in value, the magnitude of
the oscillations depending on the cause of the variations, the sensitiveness of the
bridge, the sluggish movement of the galvanometer, and the ability of the
operator. Now the galvanometer in the bridge circuit is sluggish in its movements
and unsuited to detect changes in speed lasting for a few seconds only, but the
Cambridge galvanometer used in the Lorenz circuit has a short period (5*2 seconds),
and the changes in its deflection during a measurement of resistance show that
variations in speed lasting for a few seconds only are of common occurrence.

An idea of the magnitude of these sudden changes of speed is afforded by a com-
parison of the two graphs (A) and (B), fig. 24. Graph (A) shows the variation in
the thermo-electric effects, while graph (B) shows the variation in the thermo-electric
effects plus the variations in speed. The differences plotted in graph (B) are those
taken during a measurement of a resistance. These two graphs are typical of the
results generally obtained. In all our experiments the combined variation of
thermo-electric effects and changes of speed were of about twice the magnitude of the
changes in thermo-electric effects alone, and it appears reasonable to conclude that
small oscillations in the speed were frequent. The magnitude of these oscillations
appears to be about 5 parts in 100,000. However, such fluctuations had practically
no effect on the final results.

(D) Effect of the Leads.— -It was possible that the current in the leads to and from
the coils might produce a magnetic field of sufficient intensity to affect the results.

RESISTANCE BY A METHOD BASED ON THAT OF LOEENZ. 95

This was tested by completing the main circuit through the leads only (omitting the
coils) and taking a few complete sets of observations. No effect could be measured
and we conclude that the current in the concentric leads and remaining portions of the
circuit other than the coils have no influence on our results.

(2) Normal Procedure in making an Absolute Measurement of a Resistance. — In
making a determination of a resistance in absolute measure, we determined (a) the
insulation resistance of the various parts of the circuits ; (b) the mean distance between
the mean diametral planes of the coils ; (c) the temperature of the marble cylinders ;
(d) the want of equality between the product of speed and mutual inductance and the
resistance, the value of which was desired ; (e) the temperature of the marble
cylinder ; and (f) repetition of (6).

To measure (b) and (/) we commenced with observations on the invar line standard ;
we then observed the eight plug distances and concluded with further readings on the
invar. These observations lasted about twenty minutes.

The temperatures (c) and (e) of the cylinders were taken by means of thermometers,
and the effective temperature was calculated by means of the formula given in
Section 13. In general, the difference of temperature (e) — (c) was about 2°*2 C. To
determine (d) the commutators and plugs were correctly set, the galvanometer circuit
closed, and the reversals of current, &c, made which are indicated in Section 20. At
the same time the speed was maintained constant Avithin a few parts in 100,000 and a
record of the speed taken. The time occupied was usually from 17 to 20 minutes. In
general, the first 12 reversals of current produced changes in the deflection due to a
difference Mn— R where R is the value of the standard resistance in absolute measure.
The next 8 reversals were made when R was reduced in value by 1 part in 1000 by
shunting it with another standard resistance. Then followed 24 more readings with
R unshunted; 8 with R shunted, and the final 12 measurements were made with R
again normal. The sensitiveness of the arrangement is, of course, directly proportional
to the current through the coils, and as this was not constant from day to day we
thought it best to determine it on every occasion.

Before proceeding with a measurement, the brushes were wiped with wash-leather
and the tension on the wires adjusted. The variations in the thermo-electric effects
were then observed and the petrol lubrication attended to. Bad lubrication on disc
No. 1 produced a deflection of the galvanometer in one direction, and bad lubrication
on disc No. 2 produced a deflection in the reverse direction. With a good supply of
petrol on the edges of the discs there was practically no deflection when the brushes
were in good condition. When the brushes were somewhat worn— usually after
6 runs — -it was not possible to take good observations, and rather than waste time in
making indifferent measurements we preferred to wait until new brushes had been
inserted. Careful tests of the brushes were regularly made, and it is no doubt due to
this fact that we are able to record the result of every completed measurement. At
times the thermo-electric and speed variation effects were a little troublesome, but we

96 ME, P. E. SMITH ON THE ABSOLUTE MEASUREMENTS OF A

never considered them sufficiently serious to justify us in discarding the results. It is
true that in two experiments we were not able to calculate the resistance ; in the first
of these, the apparatus for recording the speed was not put in gear and so no record
was made ; in the second, an interference with the battery connected to the motor
produced a change of speed beyond our control and we had to abandon the experiment.
In all other cases when a set of measurements was commenced, it was completed and
the result is given in this paper.

At a speed of about 17 '4 revolutions per second, the product Mn is nearly 2 x 10 6 ,
and the corresponding resistance is therefore about 0'002 ohm. We have already
described the combination of coils which gives such an effective resistance, and we
used the apparatus for its measurement on ten occasions.

To measure a resistance of 0*001 ohm, the coils on cylinders Nos. 1 and 2 were placed
in parallel with those on cylinders Nos. 3 and 4. The latter coils were found to be
equal in resistance to the former within, the limits of the errors of the measurements
made, and a division of the main current into two parts, equal within about 1 in 3000
could be ensured. In general, equality of the divided currents, within 1 per cent,
would have been sufficient. The current through the standard resistance is now twice
the mean value of the current through the coils and the resulting equation is
iMn = 2iR. When Mn — 2xlO Q , R is 0*001 ohm. This arrangement was most
convenient. A resistance of 0*001 ohm is more readily compared with 1-ohm standards
than a resistance of 0*002 ohm, and as our standard of 0*001 ohm was of thick
manganin strip, a current of 4 amperes could be passed through it without an
appreciable heating effect.

When the brushes are placed in series, a resistance of 0*01 ohm can be measured, as
the equation 5iMn = iR then holds good. Although this arrangement is very sensitive,
a slightly greater pressure is required on each brush and this frequently produced
trouble.

A sample series of readings, taken on June 7, 1913, gives a good idea of the
measurements involved in a single determination :—

June 7, 1913.

(l) Observations on invar line standard. Temperature = 15° '5 O. Lines 4-616.

Length at 15°'5 C. = 30'6016 7 cm.

Left.

Right.

Diff. (L - E).

1154-9

946-6

+ 208-3/X

1135-0

1028-0

+ 207-0

1133-4

1025-4

+ 208-0

979-4

770-9

+ 208-5

982-4

774-1

+ 208 ' 3

1035-1

825-2

+ 209-9

- Mean = + 208 * 3/x.

RESISTANCE BY A METHOD BASED ON THAT OF LORENZ.

97

(2) Observations on plugs.

Plug.

(7)

(8)
(4)

(3)
(10)

(9)
(13)

(14)

Left.

Plug.

927-3

(16)

1551-1

(15)

1052-0

(11)

328-9

(12)

1042-6

(1)

1167-6

(2)

294-3

(6)

1409-9

(5)

Right.

179-2
834-1
1185-2
2447-9
1232-3
1126-0
1199-8
757-5

Diff. (L - R).

748-1
717-0

- 133-2
-2119-0

- 189-7

41-6

- 905-5
652-4

Corr.,* d.

- 750

- 716
+ 107
+ 2094
+ 177

- 55-5
+ 887

- 669

Mean

Mean distance between the mean diametral planes of the coils

= 30-6016 7 cm. -14-2/X-208-3/X - 30*5794 2 cm.

(3) Temperature of Marble Cylinders.

(L - R) - d.

In

Before resistance

After resistance

<IO.

measurements.

measurements.

°C.

°C.

1

16-6

18-8

2

16-55

18*75

3

16-5

18-8

4

16*55

18-9

iffer

enc

C.

+ 2

•2

+ 2

•2

+ 2

•3

+ 2

•35

Mean . . . 16*5*

Mean . . . +2*2>

- 1
+ 1
-26
-25
-12
-13
-18
-16

9/*

2

7
9
5
6

-14-2/x

.-. Effective temperature = 16°-5 5 C. + 0-42 (2° -25 C.) = 17° -5 0.

* The correction is equal to the difference of the distances of the plugs from the mean diametral planes
of the coils, these distances being deduced from the metrology measurements. Thus we obtained from
these measurements: — -Distance (di) of plug 7 from centre = 9*3892 cm., distance (d 2 ) of plug 16 from
centre = 9*3142 cm. Hence, when the coils are parallel, the distance of plug 16 from plug 7 is greater
than the distance between the mean diametral planes of the coils by 9*3892 - 9*3142 = 750/x and a
corresponding correction must therefore be applied. For our purpose it is necessary to measure four
distances between four pairs of plugs, but, in practice, we measured eight distances between eight pairs of
plugs in order to obtain a check. The agreement was always good.

VOL, COXIV. — A. O

98

ME. F. E. SMITH ON THE ABSOLUTE MEASUREMENTS OF A

(4) Changes in the Deflection of the Galvanometer produced on Reversal of the

Current in the Coils.

Set No, 1.

Sensitiveness
(a).

mm.

St

mm.

mi

+ 4"

2

-36-4 -

+ o-

2

4'

2

40-0

4'

4

1

38-6

o-

2

4

•4

38-0

0-

6

2

•8

41-0

6

2

•2

37-0

2

•8

7

•0

40-0

. 7

•0

5

■4

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5

•0

1

•6

.

4

•0

4

•4

4

■4

6

•0

1

•0

4-0

1-0

Set No. 2.

mm.

+ 6
3
1

3
3
2
1
3
2
1
4

8
2

8
4
8
8
4
4
2

Sensitiveness

Set No. 3.

mm.

mm.

-38'

4

+ 2-

2

38'

4

4-

2

36

6

4'

40

•2

3-

6

41

•0

1

4

36

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2

6

37

•2

36

•2

1

•0

*

3

•8

5

•0

4

•4

3-8

Miean of Sets 1, 2, 3 = +3*2 mm.

Mean of Sets (a) and (b) = - 38 • 2 mm.

.*. Change of deflection for a diminution of the resistance of 100 parts in 100,000

= -38-2-3-2 = 41-4mm.
.-. The resistance is greater than the product Mn by — = 4-7*7 parts in 100,000.

(4) Sets of readings similar to (l) and (2) on the invar standard and the plugs were
made after the resistance measurements, hut these need not be given here. The mean
distance obtained is identical within 1/x with that already given. Such remarkable
agreement was in general found between the two sets of measurements that we
conclude the expansion of the cylinders does not affect the position of the mean
diametral planes of the coils. In such a case, with uniform expansion of the four
cylinders, the plug distances keep absolutely constant. Because of this we did not
always take a second set of readings. Constancy over seven or eight hours was,
however, rarely obtained, for the bed of the machine usually increased in temperature,
and its expansion resulted in a change in the distance between the cylinders. Of
course, the distance was frequently changed intentionally to alter the value of M.

(5) The temperature of the discs was about 17° 0. and the distance between the
brush contact circles was 167'5 cm. The speed was found from the record to be
17'3835 7 revolutions per second.

(6) Calculation of Mn. : — •

(a) The value of M x is 115893*7 when the temperature of the coils and discs is
20° C. and the distance between the mean diametral planes of the coils is 30*5785 cm.

(6) The value of M 2 is 742*4 for a distance between the brush contact circles of
167*50 cm.

KESISTANCE BY A METHOD BASED ON THAT OF LORENZ. 99

(c) When the distance between the diametral planes is increased to 30*5794 2 cm.,
M x is diminished by 3*19 ; and when the temperature of the coils is diminished to
17°*5 C, M x is reduced by 3*06.

(d) When the temperature of the disc is reduced to 17° C, M l — M 2 is increased
by 012.

(e) Hence the value of M is

M = Mx-Ma = 115893*7-742'4-3*17-3*06 + 0*12

= 115145*2 cm,

(/) M.n is therefore 115145'2 x 17*3835 7 = 200163 5 .

(7) Calculation of R«: —
We have

Hence

iMn = 2iK{l +(7'7 x 10~ 5 )}.

E = 200163 5 /2 + 7 7
= 100089 5 cm./sec.
= 0*00100089 5 ohm.

This value of E is on the assumption that the position of the mean diametral planes
has been correctly estimated from the metrology measurements. To remove the
assumption it is necessary to reverse the coils without interchanging, and this was done
after 28 measurements of the 0*001 ohm standard had been made. The effect of
reversal is very small and indicates that the assumed mean position of the diametral
planes is very nearly correct. The mean result obtained in the two positions is taken
as the value of K. When the coils Nos. 1 and 2 are used independently of Nos. 3
and 4, an appreciable difference— about 4 parts in 100,000 — is obtained on reversal of
the coils. The conclusion is that the estimated position of the mean diametral planes
of the coils Nos. 1 and 2 is incorrect by about 0*006 mm. The same is true for the
coils Nos. 3 and 4.

In Tables XX. and XXIII. we give the data relating to measurements of a resistance
of nominal value 0*001 ohm, and Tables XXI. and XXII. give the results only of
the measurements of a resistance of 0*01 ohm and an effective resistance of 0*002 ohm.

The observed values in absolute measure and the values in international ohms (new
N.P.L. Mercury Standards of Resistance) are given in Table XXIV.

Probable Errors.

The mean observational error of the results given in Table XX. is about 2 parts in
100,000 for a single observation. This error includes all the errors arising from an

*

inaccurate estimation of the distance apart of the coils, of variations in the speed, of
an erroneous estimate of the mean speed, of faulty temperature observations, and the

o 2

100

ME. F. E. SMITH ON THE ABSOLUTE MEASUREMENTS OF A

Di = Mean distance between the mean diametral planes of coils 1 and 2 and of coils 3 and 4.

M = Mutual inductance between the coils and the discs.
n = Number of revolutions per second.

E = Value of resistance in absolute measure, as deduced from the observations.

(E > Mn) = Value deduced from mean change in galvanometer deflection on reversal of current.

The values given for Di, M, &c, are not quite correct. They are subject to small corrections owing to the exact positions of the mean diametral
planes of the coils not being known. These corrections are of exactly the same magnitude in Part B of the table, but they are of opposite sign. The
mean value of E (Parts A and B) is the true one.

The distance between the brush-contact circles was practically constant and equal to 167 *5 cm.

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102

MR. F. E. SMITH ON THE ABSOLUTE MEASUREMENTS OF A

Table XXI. — -Results of Measurements of 0*01 ohm at 20°'0 C.

13.2.13

4.3.13

28.3.13

29.3.13

31.3.13

31.3.13

31.3.13

1.4.13

1.4.13

3.4.13

4.4.13

5.4.13

Mean

Part A (rings away)

Part B (rings near).

Measured

Difference from

Measured

Difference from

value of R in

mean. Parts

Date.

value of R in

mean. Parts

cm./sec.

in 100,000.
+ T8

18.6.13

cm./sec.

in 100,000.

100092 20

100093 2O

+ 3-

5

90 40

±0*

19.6.13

87eo

-1-

9

88 3 o

-2'

1

19.6.13

90 90

+ 1'

2

90 50

+ 0'

1

19.6.13

91so

+ r

8

93 20

+ 2'

8

20.6.13

8920

-0'

5

88eo

-1'

8

20.6.13

8880

-0'

9

93 40

+ 3'

21.6.13

91 6 o

+ i*

8

93 o

+ 2

•6

24.6.13

90 20

4-0'

5

9190

+ 1

•5

25.6.13

86 70

-3

•0

8850

-1

•9

26.6.13

8?50

-2

•4

87 80

-2

•6

26.6.13

90 20

+

•5

8750

-2

•9

27.6.13
Mean . . ,

89 20

-0-5

IOOO9O40

±1

'9

100089 70

±1-5

.-. Resistance = 10009 ° 40+ 1000897 ° = 100090 10 cm./sec. at 20° -OC.

Probable error of observations = 5 parts in 1,000,000.

Resistance in international ohms (N.P.L.) - 0*0100038 3 at 20° -0 0.

Difference : — Absolute measure - international measure x 10 9 = 51 ' 8 parts in 100,000.

Table XXII. — Results of Measurements at 20°'0 C. of an Effective Resistance

of 0*002 ohm.

Part A (rings away).

Part B (rings near).

Date.

Rin

cm./sec.

Rin

inter-
national
ohms.

Difference.

Abs. -int. (10 9 )

parts in

100,000.

Differ-
ence
from
mean.

Date.

28.1.13

28.1.13

4.2.13

5.2.13

6.2.13

R in

cm./sec.

200469
199457 9
200465 4

468 6
473 r

Rin
inter-
national
ohms.

200365

199354

200365

365

365

Ditierence.

Abs.- int. (10 9 )

parts in

100,000.

Differ-
ence
from

mean.

6.3.13
6.3.13
6.3.13
7.3.13
7.3.13

200479 7
472 3

472 4
478 6
478i

200368 2
368 2
368 2
368 2
368 3

55*8 '

52-1

52-1

55*2

55-0

+ 1-8
-1-9
-1-9
+ 1-2
+ 1-0

±1-6

52-0
52-0
50-2
51-8
54-3

52-0

+ 0-0
+ 0-0
-1-8
-0-2

+ 2*3

Mean . .

54-0

Mean . .

±0-'9

Probable error of observations = 6 parts in a million.

Difference -.—Absolute measure - International measure x 10 9 - (54*0 + 52*0)/2 - 53*0 parts in 100,000.

RESISTANCE BY A METHOD BASED ON THAT OF LORENZ.

103

Table XXIII. — Results of Measurements at 20°'0 0. of a Resistance of 0*001 ohm
(a) when the Coils on Cylinders 1 and 2 only were employed ; (6) when the
Coils on Cylinders 3 and 4 only were employed.

(a) Coils on cylinders 1 and 2 used.

(b) Coils on cylinders 3 and 4 used.

Date.

Ring
position.

Rin

cm./sec.

Difference
from mean.

Parts
in 100,000.

Date.

Ring
position.

R in

cm./sec.

Difference
from mean.

Parts
in 100,000.

15.4.13
15.4.13

17.6.13
18.6.13

Away

i)

Mean . . .
Near

Mean . . .

100089 7

87 4

1-1
1-2

o-i

0-2

15.4.13
15.4.13

17.6.13
18.6.13

1

Away

Mean . . .

Near
»

Mean . . .

100093 7

95 9

1 • 1
1-1

0-4
0-3

100088 6

100094 8

100092i

92 4

100089i
884

100092 2

100088 7

Grand mean = 1000904 cm./sec.

Grand mean = 100091s cm./sec.

Resistance in international ohms = 0* 010003 9 3 .

Difference : — Absolute value - international

value x 10 9 = 51 • 1 parts in 100,000.

Resistance in international ohms = 0*0100039 3 .

Difference : — Absolute value - international

value x 10 9 = 52*5 parts in 100,000.

Table XXIV.

No. of
observations

in each

position of

coils.

"

Standard.

Resistanc<

Absolute
measure.

In international
ohms.

Difference.

Parts in 100,000

fobs, x 10~ 9 ) - (int.).

28

12

5

2

2

Coils 1 and 2 used
Coils 3 and 4 used

ohm.

o-ooi
o-oi

0-002

o-ooi
o-ooi

cm./sec.
100091 6
100090io

See Tab
1000904
100091 8

0- 00100039 3
0- 0100038 3
le XXII.
0- 00100039 3
0- 00100039s

52-s

51-s
53-

51-i

52-s

The agreement is most satisfactory. Weighted mean . . 52

104 ME. F. E. SMITH ON THE ABSOLUTE MEASUREMENTS OF A

error arising from the observation of the galvanometer deflections. The probable
observational error of the mean value in absolute measure of the 0*001 ohm resistance
standard is about 3 parts in 1,000,000.

The probable error of the diametral dimensions of the coils has been estimated in
Section 13 to be not greater than 1/x plus the errors of the gauges employed.
Inspection of the results given in Table III. shows that the mean value taken as
correct differs from the results obtained in February and March, 1912, by about 1'4/x,
and from those obtained in April, 1913, by about 0°7ju. The gauges employed are
believed to be accurate within 0*5^, so that the maximum probable error of the
diametral dimensions is about +l'5/x which corresponds to a probable error in the
mutual inductance of about 8 parts in 1,000,000. This assumes that the error is of
the same sign for all the coils.

The probable error of the mean axial lengths of the coils has been estimated in
Section 13 to be about 3/x, and a change of this amount in all the coils and in the
same direction produces a change in the mutual inductance of 2 parts in 1,000,000.

Any error due to lack of knowledge of the position of the mean diametral planes of
the coils is practically eliminated by the reversals. An analysis of the plug
measurements shows that the error cannot be so great as 2 parts in 1,000,000, and
we may therefore dismiss it from consideration.

The growth in the dimensions of the coils due to the passage of the current is not
really large. The mutual inductance of the coils and brush contact circles is nearly
3 parts in 100,000 greater after the current has been left on, for 20 minutes, but the
mean mutual inductance is only about 1*5 parts in 100,000 greater than that at the
start. The error of estimation of the increase must have an exceedingly small effect
on our final results and need not be considered.

The mean diametral distance between opposite segments on the discs diminished by
0*08 mm. during our experiments. Such a change would be a serious one in the old
form of Lorenz apparatus, but in our instrument the change in the mutual inductance
due to such a reduction in the mean diameter is less than 4 parts in 1,000,000.

Evidence in favour of a small probable error is afforded by the satisfactory
agreement between the results obtained when coils Nos, 1 and 2, and 3 and 4, were
used independently. The resistance of the O'OOl ohm standard was found to be
100090 4 cm./sec. when coils Nos. 1 and 2 only were used, and 100091 8 cm./sec. when
coils Nos. 3 and 4 were used. The difference is 14 parts in 1,000,000 and part of
this is possibly due to the errors of observations, for only four observations were made
in each case.

The electrical method of setting the coils in position has been shown to be subject to
errors less than 1 part in 1,000,000 ; the magnetic susceptibility of the parts of the
apparatus, excluding the motor, is too small to be measured with the apparatus at
our disposal ■ and the effect of the motor on the mutual inductance -of the coils and
discs has been proved to be negligibly small. The errors of speed cannot be all of one

RESISTANCE BY A METHOD BASED ON THAT OF LOKENZ. 105

sign and must be quite negligible apart from a constant error in the clock rate. But
this latter is clearly impossible in the case of a standard clock the error of which is
taken daily. The daily rate was small and time comparisons were made with another
standard clock the daily rate and error of which were also known. At any hour of
the day the difference between the clocks agreed, within the possible error of the
observations, with that calculated from the errors and rates of the clocks. This
agreement is evidence that both clocks were going uniformly or that there was a
similar want of uniformity in the going of both. Such similarity is very improbable.
As an additional precaution the resistance observations were made at times ranging
from 9 a.m. to 6 p.m. but no systematic differences were observed.

The possibility of error due to our coils being of wire of finite section has not been
overlooked. The formula developed by J. Viriamu Jones gives the mutual inductance
when the coils can be treated as infinitely fine helical filaments, and small corrections
may be necessary. The case of the coils of the Ayrton-Jones current balance was
examined by Dr. G. F. 0. Searle, F.R.S., # who showed the correction to be negligible
in that instrument. In the present instance, no special treatment is necessary as the
mutual inductance calculations made during the work are sufficient to show that no
correction need be made. To illustrate this, consider the mutual inductance M of a
helical filament coinciding with the axis of the wire and the nearer brush contact
circle. Next consider two helical filaments of the same diametral dimensions as the
previous one, but let one helix be nearer to, and the other farther from, the circle by
0*25 mm. Table X. shows that the mean mutual inductance of these two helical
filaments and the circle is greater than that of the central helical filament by 2 parts
in 1,000,000. The wire with which the coils are wound is about 0*557 mm. in diameter,
so that strictly we ought to consider filaments 0'28 mm. away from the central one,,
but in view of the result obtained we think it unnecessary to calculate the small and
certainly negligible difference. Next consider two circles coaxial with the disc and at
equal distances from it, and let the diameter of one circle be greater than that of the
other by 0'556 mm., the mean diameter being 35*88 cm. At distances of 7*3135 cm..
and 23'3150 cm. the mean mutual inductance of these two circles and the circumference
of the disc does not differ by more than 2 parts in 1,000,000 from the mutual inductance
of the disc and circle of radius equal to the mean of the two previous ones (see
Table XVI.). The coil of wire may therefore be treated as a helical filament.

The determination of a resistance in absolute measure is therefore subject to a number
of small errors, the greatest of which is associated with the determination of the mean
radius of the coils. This error is probably not greater than 1 part in 100,000, and if
the remaining errors were all of the same sign it is unlikely that their sum would
exceed another part in 100,000.

We believe, therefore, that the absolute measurements of resistance which we have
made are correct within 2 parts in 100,000.

* < Phil. Trans.,' A, 207, pp. 541-544.
VOL. CCXIV. A. P

106 ME. F. E. SMITH ON THE ABSOLUTE MEASUEEMENTS OF A

The resistances which we have employed have been compared with nine new mercury
standards of resistance constructed in accordance with the Specifications of the London
Conference on Electrical Units and Standards (1908). These mercury standards of
resistance practically realise the international ohm then defined, and the agreement
between the nine standards is very good. # There are, however, certain sources of
error in the construction of such standards which must always be of the same sign, and
the probable error associated with the practical realisation of the international ohm
has been estimated to be not less than 2 or 3 parts in 100,000.

The mean of the results given in Tables XX., XXI., XXII., and XXIII. leads to
the conclusion : — ■

A resistance of 1 international ohm is equal to 1*00052 ±0*00004 ohm (10 9 cm./sec.),
the probable error ±0*00004 being approximately the sum of those involved in the
realisation of the ohm and the international ohm.

The international ohm, as defined by the London Conference on Electrical Units and
Standards (1908), is the resistance at 0° C. of a column of mercury, 14*4521 gr. in mass
of a constant cross-sectional area and of a length of 106*300 cm. As stated in the
Introduction, the cross-section of such a column is equal to 1 sq. mm. or nearly so.

Since the international ohm is equal to 1*00052 ±0*00004 ohms, the mass of the
column of mercury of the same cross-sectional area as the international ohm and having

a resistance of 1 ohm will be ^ — = 14'4446±0'0006gr.,fwhilethe length

of the column will be 106 ' 300 = 106*245 + 0*00004 cm.f

r00052±0*00004

We may sum up our results by stating that :—

The ohm 10 9 cm./sec. is represented by the resistance at 0° C. of a column of mercury
14*4446 ±0*0006 gr. in mass, of a constant cross-sectional area (the same as for the
international ohm) and having a length of 106*245 ±0*004 cm.

The Historical Introduction shows a number of determinations, notably those of
Rayleigh (corrected values marked (S) Table I.), Glazebrook (corrected value (S)
Table I.), Wiedemann, Dorn, and Himstedt, in close agreement with that now
obtained. These results are as follows : —

1882, Kayleigh 106*26 cm.

1882, Glazebrook 106*25

1883, Kayleigh 106*24

1885, Wiedemann 106*265

1889, Dorn 106*243

1892, Himstedt 106*259

35

* ' Keport of the National Physical Laboratory for 1912.'

t The probable errors in these two values are so related that an error in either value is necessarily
associated with an equivalent proportionate error in the other.

RESISTANCE BY A METHOD BASED ON THAT OF LORENZ. 107

On the whole, the remaining results in Table L give the length of the column of
mercury representing the ohm as greater than 106*25 cm., and while a discussion of
the methods and apparatus might do much to explain some of the differences, much
greater detail of the apparatus than is readily accessible is necessary for this to be
done.

The ohm and the international ohm differ by about 5 parts in 10,000, and since the
ampere (lO -1 C.G.S. unit) has been realised with considerable accuracy, we may
express the electromotive force of the Weston normal cell in absolute measure. The
value found in 1908 by Ayrton, Mather and Smith at the National Physical
Laboratory for the E.M.F. of the Weston normal cell in terms of the ampere
(10" 1 C.G.S. unit) and the international ohm is 1*01830 volts at 17° C, with a
probable error of 2 parts in 100,000. The deduced value at 20° C is 1*01818 volts.
Since that time measurements have been made by Janet, Laporte, and Jouast # at
the Laboratoire Central d'Electricite ; by Prof. GuiLLETf and Prof. Pell at, f by
Haga,J and by Rosa and Dorsey§ at the Bureau of Standards. The results are : — ■

Ayrton, Mather, and Smith 1*01818

Janet, Laporte, and Jotj ast 1*01836

Gijillet . . , , . . . 1*01812

Pellat . . . 1*01831

Haga 1*01825

Rosa and Dorsey 1*01822

Mean 1*01824 at 20° C.

These results include the errors of the resistance standards employed as well as the
errors of the determination of the current in absolute measure. In addition small
differences existed between the Weston cells. Considering all these circumstances
the agreement is very remarkable and testifies to the great care taken in the measure-
ments. There appears to be little doubt that the value 1*01824 at 20° C. is correct,
within 1 part in 10,000. We conclude that the value of the cell in volts (10 8 C.G.S.
units) is 1*0188 ± '0001 at 20° C. This value may serve for the present for those
engaged in absolute measurements.

Section 24. — Conclusions.

From the measurements recorded in the previous sections, we conclude that the
instrument we have described may be used for absolute measurements of resistance

* 'Bull, de la Soc. Internat. des Electriciens ? (2), vol. 8, p. 459, 1908, and ' Comptes Rendus/ 153,
p. 718, 1911.

t 'Bull, de la Soc. Internat. des Electriciens,' 1908.

| < Konink Akad. Wetensch. Amsterdam Proc.,' p. 587, 1910.

§ 'Bull. Bureau of Standards/ vol. 8, p. 269, 1912.

P 2

108 ME. F. E. SMITH: ABSOLUTE MEASUREMENTS OF A RESISTANCE, ETC.

with a precision satisfying all present demands whether purely scientific or technical.
We believe the instrument fully realises the desires of those who were responsible for
such measurements being made, and the results justify Lord Rayleigh's belief that
the ohm, as defined in absolute measure, can be realised with a precision comparable
with that of the international ohm. The instrument can be used at any time ; the
dimensions of all its parts can be checked when desired, the probable error associated
with a single measurement is small, and the observations do not unduly tax the
experimenter. We have formed an estimate, based on the measurements already
made, of the time necessary to devote to a complete re-determination supposing the
cylinders to be stripped of the coils. The re-winding of the coils would occupy three
days, the metrology measurements would extend over six days, and sufficient
resistance observations could be made in eight more days. Absolute measurements of
resistance may therefore be placed in the front rank of precision measurements.

In conclusion, we desire to express our sincere thanks to the Drapers Company of
London for providing a large sum of money towards the cost of the instrument, and
to Sir Andrew Noble, F.R.S., for his generous help with the heavy metal work.

Our most hearty thanks are hereby tendered to our Director, Dr. R. T. Glazebrook,
C.B., F.R.S., who has not only given his very valuable help and advice throughout
the work, but has fully appreciated the many difficulties which have arisen and which
required much time and patience to remove.

Our best thanks are also due to Lord Rayleigh for his keen interest in the
investigation, to Dr. Stanton for superintending the turning of the marble
cylinders, and to many of the staff of the National Physical Laboratory, particularly
Mr. A. Campbell and Mr. Dye, for suggestive aid throughout the investigation.

Fig. 3.

Fig. 4.

To face p. 40.

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